Residual stresses can meaningfully influence on the operation of a part. They are almost created by all fabrication processes. In this study, slitting method was used to obtain the residual stress profile through the thickness of equal-channel angular rolled aluminum strips. Furthermore, uncertainty analysis of the measured residual stresses was performed. The measurement and model uncertainties were considered in the uncertainty analysis, and the effect of each one on the total uncertainty was investigated. Besides, to study the through-depth residual stress distribution numerically, finite element simulation of equal-channel angular rolling process in route C was done. In route C, the strip should be rotated around the longitudinal axis by 180° after each successive pass. The results showed the important role of both measurement and model uncertainties in the calculation of total uncertainty. The maximum tensile residual stresses of the control, 1-pass and 2-pass samples were 7.59, 64.4 and 85.11 MPa, respectively, and the root mean square total uncertainty of them were 1.47, 2.43 and 5.12 MPa, respectively. There was a good agreement between experimental and numerical results.
The measurement of residual stress using the deep-hole drilling method relies on the evaluation of the distortion of a hole in a plate under the action of far-field direct and shear stresses. While closed-form solutions exist for the isotropic materials, in previous work for orthotropic materials, finite element analysis has been used to find the distortion. In this technical note, Lekhnitskii’s analysis is used to find closed-form solutions for the distortion of a circular hole in an orthotropic plate. The results are compared with those of finite element analysis for a range of material properties with excellent agreement.
To explore the mechanical properties of braided wire rope, relevant theories of differential geometry are applied to deduce the space curve parametric equation of braided wire rope, specific to the structural features of the rope. On this basis, a geometric entity model of YS9-8 x 19 braided wire rope is established. Through mesh generation, a finite element model of braided wire rope is obtained. Constraints and loads are applied for numerical simulation calculations. The numerical simulation results are analyzed to reveal the stress and deformation distribution rules of the rope strands along the rope axis direction and on the cross sections of strands. Tensile tests of YS9-8 x 19 steel wire ropes are performed. The test data and the analogous simulation results coincide, verifying the rationality of the model. The study provides theoretical bases for subsequent frictional wear and life studies on this steel wire rope.
The horizontal perforated sheet metal plates are commonly used in the process industries as trays in distillation columns, important internal parts for fractionating the input liquid mixture. Normally, the operating performance of such trays is satisfactory. However, cases have been reported of abnormally high levels of tray vibration during operation at particular conditions. The trays then experienced fatigue cracking accompanied by the loosening of bolts and fixings, which led to expensive failures. The excitation of structural resonance was suspected as a component in flow-induced vibration. Using linear stress superposition, a simple but robust analytical method is developed to provide high-quality predictions for the stress and strain distributions for in-plane loaded thin perforated plates with periodic hole arrangements. This approach is built on the classical solution for the elastic stress field around a single circular hole in a large plate. The perforated plates with square penetration patterns are investigated in this article, although the same approach is applicable to any regular penetration pattern. Stress concentration factors as well as the effective elastic constants, which can be used to describe the bending properties of the perforated plates, are then verified against both the established theoretical solutions and the results from finite element simulations. Excellent agreement to both previously published physical experiments and complex modelling is observed in all cases, with small-to-medium (up to 40%) hole-area fraction. The proposed analytical method is much simpler and computationally efficient than finite element analysis. The computed effective elastic constants are used in a finite element modal analysis to estimate the free vibration frequencies of a stiffened distillation column tray example; the first 30 vibration modes are found to be almost uniformly distributed between 25 and 70 Hz, which matches the vibration frequency range reported from plant operations.
In the present work, the non-linear post-buckling load–deflection behavior of tapered functionally graded material beam is studied for different in-plane thermal loadings. Two different thermal loadings are considered. The first one is due to the uniform temperature rise and the second one is due to the steady-state heat conduction across the beam thickness leading to non-uniform temperature rise. The governing equations are derived using the principle of minimum total potential energy employing Timoshenko beam theory. The solution is obtained by approximating the displacement fields following Ritz method. Geometric non-linearity for large post-buckling behavior is considered using von Kármán type non-linear strain-displacement relationship. Stainless steel/silicon nitride functionally graded material beam is considered with temperature-dependent material properties. The validation of the present work is successfully performed using finite element software ANSYS and using the available result in the literature. The post-buckling load–deflection behavior in non-dimensional plane is presented for different taperness parameters and also for different volume fraction indices. Normalized transverse deflection fields are presented showing the shift of the point of maximum deflection for various deflection levels. The results are new of its kind and establish benchmark for studying non-linear thermo-mechanical behavior of tapered functionally graded material beam.
Numerical and experimental investigations of autogenous plasma arc welding of thin titanium alloy of 2 mm thick and modelling the temperature distribution for predicting the weld bead geometry are presented. The finite element code COMSOL Multiphysics is employed to perform non-linear unsteady heat transfer analysis using parabolic Gaussian heat source. Temperature-dependent material properties such as thermal conductivity, density and specific heat are used to enhance the efficiency of simulation process. A forced convective heat transfer coefficient was used to account for the effect of convection. The experimental trials were conducted by varying the welding speed and current using Fronius plasma arc welding equipment. The simulation results are in good agreement with the experimental results.
Data about a muscle’s fibre pennation angle and physiological cross-sectional area are used in musculoskeletal modelling to estimate muscle forces, which are used to calculate joint contact forces. For the leg, muscle architecture data are derived from studies that measured pennation angle at the muscle surface, but not deep within it. Musculoskeletal models developed to estimate joint contact loads have usually been based on the mean values of pennation angle and physiological cross-sectional area.
Therefore, the first aim of this study was to investigate differences between superficial and deep pennation angles within each muscle acting over the ankle and predict how differences may influence muscle forces calculated in musculoskeletal modelling. The second aim was to investigate how inter-subject variability in physiological cross-sectional area and pennation angle affects calculated ankle contact forces.
Eight cadaveric legs were dissected to excise the muscles acting over the ankle. The mean surface and deep pennation angles, fibre length and physiological cross-sectional area were measured. Cluster analysis was applied to group the muscles according to their architectural characteristics. A previously validated OpenSim model was used to estimate ankle muscle forces and contact loads using architecture data from all eight limbs.
The mean surface pennation angle for soleus was significantly greater (54%) than the mean deep pennation angle. Cluster analysis revealed three groups of muscles with similar architecture and function: deep plantarflexors and peroneals, superficial plantarflexors and dorsiflexors. Peak ankle contact force was predicted to occur before toe-off, with magnitude greater than five times bodyweight. Inter-specimen variability in contact force was smallest at peak force.
These findings will help improve the development of experimental and computational musculoskeletal models by providing data to estimate force based on both surface and deep pennation angles. Inter-subject variability in muscle architecture affected ankle muscle and contact loads only slightly. The link between muscle architecture and function contributes to the understanding of the relationship between muscle structure and function.
The stress–strain behaviour of skeletal muscle is affected by many factors, leading to varied results reported in the literature. This article examines how the physical dimension of samples in in vitro compression tests affects the muscle stress for a given stretch ratio, in both quasi-static and dynamic loading. It is proposed that physically larger samples display a higher stress response due to the greater inclusion of complete muscle fascicles and also a reduction in percentage fluid exudation during compression. In the case of quasi-static loading, this was evaluated by testing nominally cubic samples of fresh and aged porcine tissue of characteristic lengths between 10 and 40 mm in compression at 0.05%/s strain in the fibre and cross-fibre directions using a Zwick Z005 universal testing rig. For the dynamic tests, a custom instrumented drop tower test rig was used to achieve average strain rates of 12,500%/s, and the stress responses at stretch ratios of
This article shows an experimental validation of the volume conservation assumption (zero plastic volume change assumption) for aluminum alloy (AA6000) sheet metal. A series of tensile tests were conducted. During the tensile tests, an optimized digital image correlation setup was used to simultaneously measure three principal strain components. The experimental results show that, at locations outside the necking band, AA6000 strictly follows the zero plastic volume change assumption throughout the duration of the test. Inside the necking band, AA6000 follows the zero plastic volume change assumption in the elastic range and early plastic range. However, before failure, a visible volume strain increase can be found inside the necking band, which shows that, in the deep plastic zone, AA6000 does not always follow the volume conservation assumption. The experiment plan, measurement setup optimization, experimental results and data analysis are shown in detail.
Finite element model updating is a powerful technique to inversely identify material behaviour. A profound understanding of plastic anisotropy of sheet metal is crucial in controlling complex sheet forming applications through finite element simulations. In this contribution, a generic stereo finite element model updating approach combining stereo digital image correlation and finite element model updating is described to identify the plastic anisotropy of sheet metal DC06 which is represented by Hill’s 1948 yield criterion. The feasibility of stereo finite element model updating is illustrated by applying the proposed method to an Erichsen bulging test. Additionally, it is found that the unknown friction coefficient between the punch and the sheet can be simultaneously identified. Finally, the reliability of the identified parameters is scrutinized.
A total of two computational procedures have been developed in the commercial finite element software codes Sysweld and ABAQUS to analyse and predict the residual stress state after the repair of small weld defects in thin structural components. The numerical models allow the effects of the repair to be studied when a pre-existing residual stress field is present in the fabricated part and cannot be relieved by a thermal treatment. In this work, the modelling strategies are presented and tested by simulating a repair of longitudinal welds in thin sheets of Inconel 718. Although the numerical strategies in the two codes are intrinsically different, the results show a significant agreement, predicting a notable effect imposed by the initial residual stress.
The hole drilling method is a well-known technique for the determination of non-uniform residual stress profiles by measuring relaxation distortions caused by the presence of the hole. The integral method, an inverse calculation technique on which the hole drilling method is based, assumes linear elastic material behaviour and is therefore limited to the measurement of residual stresses below 60% of the yield strength. The aim of this study is to investigate the effects of elastic–plastic material behaviour on the determined non-uniform residual stress profile when the residual stresses exceed the given 60% limit. To this end, compressive residual stress profiles, as they are typically induced by laser shock peening, are investigated using finite element simulations followed by an analysis with the integral method. The obtained results from the analysis are compared to the applied residual stress profiles. An evaluation of the deviation between these two profiles provides detailed insight into the expected error as a function of hole drilling depth and the ratio of residual stress magnitude to yield strength. As an additional benefit of the presented approach, it also provides an indication of the range of depth at which the non-uniform residual stress profile should be corrected to reduce measurement error.
According to acoustoelastic theory, ultrasonic wave velocity varies as a function of the state of stress in a body. In ferromagnetic materials, stress alters magnetic domain walls created by cyclic magnetic excitation and affects the amplitude of magnetic Barkhausen noise signals. In this work, both these properties are used to measure different levels of stress in specimens of API 5L X70 steel. Time of flight of ultrasonic critically refracted longitudinal (Lcr) waves and magnetic Barkhausen noise are measured and compared using three parameters: sensitivity, linearity, and dispersion. The results show that while magnetic Barkhausen noise is much more sensitive to variations in stress, the time of flight values fit a linear curve better. Also, for the ultrasonic technique, dispersion between the curves for the different specimens is lower. For both techniques, measurement dispersion in the specimens when no stress is applied is high. The findings of this study can be used to indicate the limits within which each technique can be used and to help decide when it is more appropriate to use one technique rather than the other.
In this article, the effect of notches on the mechanical response of superelastic NiTi shape memory alloy is studied experimentally. Due to the complexity and feasibility in designing and manufacturing, double-edge semi-circular notches were chosen as the investigating features, and a dimensionless parameter was introduced to ease the discussion. With the help of in situ digital image correlation, both local and global mechanical responses were analyzed in the study. From the local mechanical response of notched specimens, the -shaped intersection of the transformation bands and the V-shaped transformation fronts were observed; from the global mechanical response of notched specimens, the intermediate stage prior to the upper stress plateau was identified. These observations shed light on the ongoing relevant study on the mechanical characteristics of NiTi shape memory alloy with complex geometry.
Prediction of the fatigue lives of components in engineered products is an important area of study; fatigue failure of a component may have product safety implications. Nearly all components contain stress concentration features and fatigue cracks will typically develop from these stress concentrations. Therefore, it is important that fatigue life prediction methods take into account the presence of stress concentrations. This article compares two methods of correlating fatigue test results between smooth and notched specimens in order to be better able to predict the fatigue lives of full-scale components. The first method uses the Neuber analysis approach to predict the strain range and mean strain at the root of the notch; the second uses elastic-plastic finite element analysis of the notched specimens. Two circumferentially notched specimen geometries are considered, with Kt values of 2.19 and 3.43. The analyses show that the Neuber method under-predicts the fatigue lives of the notched specimens, whereas a closer correlation is obtained using the finite element models. This is explained in terms of the different levels of constraint on yielding in a circumferentially notched specimen relative to the pure shear loading that is the basis of the Neuber analysis. Four methods of enhancing the finite element correlations are described. The first uses a method developed by Peterson to define a fatigue stress concentration factor. The second uses a mean stress and stress range approach developed by Smith, Watson and Topper. The third uses a critical distance approach developed by Pluvinage. The final method takes into account the volume of highly stressed material at the root of the notch using an approach first described by Waters and Norris to define a fatigue stress concentration factor. This approach has many parallels with the strain energy density approach.
Problems of stress concentration around a spherical cavity in transversely isotropic materials under pure shear are solved by the equivalent inclusion method. A method previously devised for finding the solution requires introducing harmonic functions in three different spheroidal coordinates and this complicates the analysis. Compared with that approach, the present method is simpler and more transparent; any possible error can be easily detected as the solution procedure requires only elementary algebraic manipulations. Stress concentrations around the cavity are obtained in explicit mathematical expressions and maximum hoop stress can be conveniently calculated. Numerical results of several transversely isotropic materials (zinc, magnesium, β-quartz, and poled barium titanate) are tabulated and graphically displayed to highlight the nature of the solution.
This work presents a one-dimensional harmonic finite element for the transient elasto-plastic analysis of axisymmetric structures loaded by non-axisymmetric thermal and mechanical loads. The one-dimensional element exploits a semi-analytical approach, based on Fourier series decomposition of the applied loads. The initial stress method is used for the non-linear solution of elasto-plastic analysis. As a case study, the proposed one-dimensional harmonic element is applied for modelling a two-dimensional circle under thermal and mechanical loadings rotating over its surface, which is used as an approximation of a work roll in hot strip rolling. With the one-dimensional harmonic element, the cyclic thermo-mechanical behaviour of the work roll can be simulated by considering localized plasticity caused by thermo-mechanical loads representative of strip and back-up roll. Compared to two-dimensional models already used in the literature, the one-dimensional element allows a significant reduction in the computational time to be achieved; it follows that the whole transient thermo-mechanical response can be simulated, thus permitting a more complete evaluation of the stress–strain response that is necessary for fatigue life assessment.
AA-6061 (T6) aluminum alloy sheet is used extensively for structural applications in various automotive and aerospace industries due to its excellent mechanical and physical properties. Due to lower formability of this material in age-hardened (T6) condition, forming of complex-shaped components is a major challenge. Forming behavior of the sheet was studied in T6 condition using limit dome height tests by experiment and finite element method for three different sheet directions (rolling direction, inclined direction (ID) and transverse direction). Strain path diagrams were obtained from the experimental limit dome height tests and finite element method simulations from drawing to stretching region, and the results were compared for all the sheet directions. Forming limit diagrams were plotted using strain localization and fracture criteria from experimental and simulated strain path curves. Effect of plastic anisotropy on crack propagation direction was studied using finite element method, and it has been found that the direction of crack propagation was strongly dependent on plastic anisotropy ratio ("r" value) of the sheet in biaxial strain paths.
This article shows the results of finite element analyses of small punch creep testing of a P91 steel at 600 °C using two different approaches to model the friction between the specimen and the punch. The numerical results obtained using the ‘classical’ Coulomb friction model (i.e. constant friction coefficient) have been compared with those obtained by a more modern formulation, which takes into account the effects of local loading conditions, that is, the contact pressure, between the contacting bodies (the small disc specimen and the punch) on the coefficient of friction. The aim of the work is to investigate the effects of the friction formulation used for the calculations on the numerical results representing the output of the test, that is, the variation of the punch displacement versus time and the time to rupture. The calculations, carried out for various load levels, showed that the friction coefficient is not constant at all positions on the contacting surface between the punch and the specimen during the deformation process. The maximum value for the coefficient of friction is reached at the contact edge, which is a very important region in the specimen, because this is the position at which most of the creep deformation occurs. As expected, the displacement versus time curve (that is usually the only output obtained from experimental small punch creep testing) is affected by friction formulation which is used, as this directly influences the stress and strain fields in the specimen.
A prospective method for structural health monitoring of engineering materials and structures is based on embedded strain sensors in the form of electrically conductive carbon rovings. This article presents the results of the application of carbon rovings and the development of flexible textile fabrics based on these rovings for measuring the deformation in engineering materials, including concrete and polymer- and cement-based composites. The possibility of using carbon rovings as a strain sensor is demonstrated via measurements in tensile and four-point bending tests. The experimental setups and methods for measuring the electrical resistance of carbon roving as a function of strain in the roving, concrete, and composites are described. A good correlation has been found between the electrical resistance–strain curve of the carbon roving (used as a calibration curve) and the measurements in the concrete and polymer composites from tensile tests. The difference in the character of the flexural behavior and the electrical signal in the carbon roving cement-based composite, affected by the stitch type and shape of the carbon roving cross section in textile fabric, was found through four-point bending tests.
While adhesion reduction due to roughness is not surprising, roughness induced adhesion remained a puzzle until recently. Guduru and coworkers have shown a very convincing mechanism to explain both the increase of strength and of toughness in a sphere with a concentric single scale of waviness. Kesari and coworkers later showed some very elegant convenient asymptotic expansions of Guduru’s solution. This enhancement is very high and indeed, using Kesari’s solution, it is here shown to depend uniquely on a Johnson parameter for adhesion of a sinusoidal contact. However, counterintuitively, it leads to unbounded enhancement for conditions of large roughness for which the Johnson parameter is very low. Guduru postulated that this enhancement should occur after sufficiently large pressure has been applied to any spherical contact. Also, although the enhancement is limited to the Johnson, Kendall and Roberts (JKR) regime of large soft materials with high adhesion, the DMT limit for the smooth sphere is found otherwise. However, for hard materials, even the Derjaguin, Muller and Toporov (DMT) limit for the smooth solids is very hard to observe, which suggests that adhesion reduction is also not yet well understood.
The limitations of the assumption of simply connected area are here further discussed, and a well-known model for hard particles in contact with rough planes due to Rumpf is used to show that, in the range where an unbounded increase is predicted, orders of magnitude reduction is instead expected for rigid solids. We suggest that Guduru’s model may be close to an upper bound for adhesion of rough bodies, while the Rumpf–Rabinovich model may be close to a lower bound.
The offset between the hole and the centre of the strain-gage rosette is unavoidable, although usually small, in the hole-drilling technique for residual stress evaluation. In this article, we revised the integral method described in the ASTM E837 standard and we recalculated the calibration coefficients. The integral method was then extended by taking into account the two eccentricity components, and a more general procedure was proposed including the first-order correction. A numerical validation analysis was used to consolidate the procedure and evaluate the residual error after implementing the correction. The values of this error resulted limited to a few percentage points, even for eccentricities larger than the usual experimental values. The narrow eccentricity limit claimed by the standard, to keep the maximum error lower than 10%, can now be considered extended by approximately a factor of 10, after implementing the proposed correcting procedure, proving that the effect of the eccentricity is mainly linear within a relatively large range.
An analytical solution for torsional analysis of constrained open-section members, which can estimate the variation of the axial displacement, the normal and shearing stresses along the beam and across the cross section, is important and is the main goal of this article. A new formulation for constrained torsional analysis of open-section members is presented. In the formulation, cross sections with curved corners can be analyzed. The cross section is decomposed into some straight and curved segments with uniform thickness. This decomposition makes it possible to solve the governing equations in each segment analytically. The method can predict the stress concentration at reentrant corners of the cross section with an acceptable accuracy. Specific formulas for channel beams and tubes with a longitudinal slot are also derived. Accuracy of the presented method is verified by comparing the obtained results with the three-dimensional finite element method solutions with a fine mesh. Numerical investigations show that the obtained formulas give relatively accurate results for thin to moderately thick-walled open cross sections.
The main limitation of digital image correlation is the remarkable noise affecting the digital image correlation–computed strain distributions. Neither manufacturers of digital image correlation systems nor the literature provide guidelines for optimal filtering of digital image correlation strain distributions. However, filtering is also associated with loss of information (smoothing of the strain gradients). We systematically explored different filtering strategies to reduce noise while minimizing the loss of information in the digital image correlation–computed strain distributions. The first filtering strategy was directly applied to the acquired images that were then fed to the digital image correlation software. Median adaptive low-pass filters and notch filters were used to eliminate noise: both strategies increased (rather than reducing) the noise in the digital image correlation–computed strain distributions. The second strategy explored was a Gaussian low-pass filtering of the strain distributions. When the optimal cutoff frequency was selected, the noise was remarkably reduced (by 70%) without excessive loss of information. At the same time, when non-optimal cutoff frequencies were used, the residual noise and/or loss of information seriously compromised the results. Finally, image combination techniques were applied both to the input images and to the strain distributions. This strategy was extremely time-consuming but not very effective (noise reduction <10%). In conclusion, the only truly effective noise reduction strategy, if measurements are carried out using commercial closed software, consists in filtering the strain distribution.
A shrink-fit sample is manufactured with a Ti-8Al-1Mo-1V alloy to introduce a multiaxial residual stress field in the disk of the sample. A set of strain and orientation pole figures are measured at various locations across the disk using synchrotron high-energy X-ray diffraction. Two approaches—the traditional
Accurate characterization of delamination damage and evolution plays a significant role in studying the failure behaviors of composite laminates. In the present research, both acoustic emission and digital image correlation technology are used to simultaneously monitor the buckling process of multi-delaminated composites under compression. Three kinds of composite specimens are carried out to investigate the influence of delamination lengths and positions on the compressive behaviors of the composites. Meanwhile, the buckling load, micro-displacement fields of interfacial zone and acoustic emission response characterizations are also obtained. The results indicate that acoustic emission parameters such as hits, amplitude, duration and relative energy are correlated with the damage process of composite specimens, while the critical damage deformation of delamination regions is clearly exhibited from digital image correlation results. Furthermore, the buckling behaviors are significantly influenced by the thickness of sub-layer and the lengths and positions of delaminations. The complementary nondestructive testing technologies combining acoustic emission with digital image correlation are beneficial for in situ damage monitoring of the composites.
In the surface strain measurement, different settings of the variables applied in digital image correlation procedure give rise to different measurement error levels. This article discusses how the variable settings affect the error, and meanwhile put forward a method to optimize the variables. The deformation of the synthetic reference image for digital image correlation procedure is determined by a finite element simulation of a tensile test under certain loading condition. The digital image correlation variables concerned in this article contain the subset size, step size, shape function and strain window size. Moreover, a genetic algorithm is developed to optimize the setting of these variables, and their sensitivities are further analysed to clarify the different impacts of each parameter on the total measurement error. As demonstrated by the results, the measurement can be improved to a more satisfactory level after the optimization to the digital image correlation processing variables.
In this article, a semi-analytical method to estimate elastic follow-up factor as input to estimate the transient creep C(t) parameter under secondary loading is presented and validated against finite element results for a cracked two-bar structure under constant displacement loading. Predicted values of C(t) agree well with the finite element results for both elastic-creep cases and for elastic-plastic cases with the same creep and plastic hardening exponents. For elastic-plastic-creep cases with different creep and plastic hardening exponents, the proposed method gives good predictions at long time but can under- or over-predict C(t) at short time.
Split sleeve cold expansion is a widely used process in the aerospace industry to enhance the fatigue life of rivet holes in the aircraft structures. In the experimental investigation presented in this article, the full-field in-plane residual strains and the out-of-plane surface deformations around open cold-expanded holes were measured using stereoscopic digital image correlation in aluminium specimens of two different thicknesses giving thickness-to-diameter ratios of 0.25 and 1. The results demonstrate that the mechanics of hole deformation is significantly different for the thick and thin specimens. The specimens of 1.6 mm thickness underwent a combination of global bending and significant local warping during the cold expansion process. This localised warping caused a decrease in the minimum principal residual strains close to the edge of the hole, which cannot be predicted by the existing theoretical models as they do not account for the complex out-of-plane deformations that have a significant influence on the shape of the resulting residual strain profiles. In contrast, 6.35-mm-thick specimens did not bend globally mainly because of the higher second moment of area of their cross sections. The material close to the hole edge bulges out from both the faces of the specimen as a result of plastic deformation during the cold expansion process and the out-of-plane deformations are much more localised and lower in magnitude in comparison to the thin specimens. The plastic zone developed around the expanded hole is more axisymmetric and larger in size for the thick specimens. These results imply that the existing split sleeve cold expansion process is not as effective in creating a uniform compressive residual elastic stress field around the fastener holes in thin as it is in the thick specimens.
This article investigates the possibility of failure by crack-opening mode III (out-of-plane shearing) in sheet–bulk metal forming processes. The investigation makes use of experimentally and theoretically determined fracture-forming limits of aluminium AA1050-H111 sheets with 1 mm thickness, experimental tests in incremental ploughing with a roll-tipped tool and numerical simulation using a commercial finite element programme. Results show that incremental ploughing of thin sheets with a roll-tipped tool under large indentation depths gives rise to transverse cracks that are triggered at the upper groove surface and propagate downward across thickness along an inclined direction to the sheet surface. In contrast to sheet–metal forming processes that only fail by fracture in crack-opening modes I and II, sheet–bulk metal forming processes present the unique ability of failing in all three possible crack-opening modes, namely, in mode III that is typical of bulk metal–forming processes.
The residual stress analysis is a well-established method for predicting fatigue failures of mechanical components. Within industrial constraints, the X-ray diffraction is a technique usually applied to measuring a small spot of the workpiece surface. This punctual and averaged outcome does not allow the proper representation of the residual stress. The objective of this study is to define a feasible method for assessing the heterogeneity of the surface residual stress state. The proposal is based on the theoretical relationship between the deviation of the residual macrostress and the intensity of the microstress. Steel shot peened gears were produced and their microstresses were assessed by means of the diffraction profiles broadening. The reference database was composed of topography measurements, metallographic analyses and residual macrostress maps. The stress heterogeneity was reasonably correlated to the intensity of the Gauss integral breadth. Applied to ground parts, the correlation’s parameter filled a comprehension gap between the measured residual stress intensity and observed contact fatigue failures. Using the same data from the macro residual stress measurement, the method proved to be feasibly applied. Moreover, by providing a deviation perspective to the residual stress state, the heterogeneity assessment enhances the analysis of a fatigue failure.
This article presents a methodology for the treatment of uncertainty in nonlinear, interference-fit, stress analysis problems arising from manufacturing tolerances. Image decomposition is applied to the uncertain stress field to produce a small number of shape descriptors that allow for variability in the location of high-stress points when geometric parameters (dimensions) are changed within tolerance ranges. A meta-model, in this case based on the polynomial chaos expansion, is trained using a full finite element model to provide a mapping from input geometric parameters to output shape descriptors. Global sensitivity analysis using Sobol’s indices provides a design tool that enables the influence of each input parameter on the observed variances of the outputs to be quantified. The methodology is illustrated by a simplified practical design problem in the manufacture of automotive wheels.
Failure of metallic structures operating under shock loading is a common occurrence in engineering applications. It is difficult to estimate the response of complicated systems analytically, due to structure’s dynamic characteristics and varying loadings. Therefore, experimental, numerical, or a combination of both methods is used for evaluations. In this study, test pieces made of two different materials are subjected to shock loads stemming from firing of a Gatling gun. Strain measurements are made, and finite element analysis of the test piece is performed. As a result of this study, strain energy density theory is applied to predict the shock failure of metallic structures.
A common feature of uniaxial high-temperature tension tests, and to a certain extent compression tests, performed using a Gleeble thermomechanical testing system that employs direct resistance heating for the characterisation of the rheological behaviour of materials is longitudinal and radial thermal gradients. The aim of this article is to experimentally quantify the axial thermal gradients for a given tensile specimen geometry of free cutting steel during heating and deformation, and design a modelling methodology to simulate their influence on the strain distribution as compared to the assumption of isothermal heating and deformation. For this purpose, a feedback algorithm was developed to control the electric current input in a similar manner to that applied by the Gleeble testing system, which implemented via the UAMP user subroutine in ABAQUS for use in electro-thermal simulations of the direct resistance Joule heating used by the Gleeble testing system. The predicted temperature fields were compared with the temperature distributions recorded experimentally along the gauge section of the tensile specimens. Finite element simulations of Gleeble tensile tests were carried out under isothermal conditions and using the temperature distributions calculated by the feedback algorithm for a range of strain rates and temperatures in order to evaluate the difference in predicted stress state. The results show that an isothermal assumption should only be used conservatively in finite element simulation of the Gleeble thermomechanical test employing direct resistance heating to avoid significant errors.
This article presents development of a damage-coupled viscoplastic constitutive model with temperature consideration. The model is subjected to an explicit nonlocal treatment within the characteristic length that is not limited to one local element as conventional ones. Temperature dependence of material behavior is incorporated into the model to account for the material property degradation at elevated temperature. A test program to determine the correlation between material parameters and temperature is also presented. The nonlocal damage-coupled viscoplastic material model is implemented in a commercial finite element program ABAQUS through its user-defined material subroutine UMAT using a semi-implicit time integration scheme. The model is applied to predict the behavior of 63Sn37Pb soldered structure. The mesh sensitivity of the model is discussed, as well as the efficiency of deduced consistent tangent modulus.
To ensure a reliable connection between two pipe sections, an initial make-up is applied to the threaded connections to induce a favorable stress state. Using finite element analysis techniques, it is possible to predict the internal strains and stresses of the connection when torque is applied. This article presents the outline of an experimental setup, which allows to directly validate the occurring strains together with the torque versus turn diagram and indirectly the contact pressures. The strains are measured by means of digital image correlation and strain gages. Both methods provide similar results and comply with the predicted finite element analysis strains when taper mismatch is taken into account. In an effort to qualitatively validate the simulated contact pressures, the temperature of the box is measured during make-up by means of infrared monitoring. The maximum temperature increase occurs near the vanishing threads where contact pressures are larger. Despite promising results, no decisive validation for the contact pressures could be obtained.
Lower bound limit load solutions for extended surface cracks in plates with free ends (pin-loaded) under combined biaxial positive/negative force/stress and positive/negative through-thickness bending are developed based on the lower bound limit load theorem and both Tresca and Mises criteria. An existing Mises limit load solution for extended surface cracks in plates with fixed ends under combined biaxial tension and positive moment is extended to general solutions for combined biaxial positive/negative force/stress and positive/negative through-thickness bending moment. Corresponding reference stress expressions are also derived and presented.
Uncoupled thermo-mechanical finite element analyses, using ABAQUS, are conducted to determine residual stresses created by quenching of 316 stainless steel and AISI 1020 low-carbon steel cylindrical bars. It is found that the magnitude of the residual stresses can be determined from an estimate of the thermal strain difference created in the bars during quenching. It is shown that the strain difference is a function of the Biot and Fourier numbers and the initial and final quench temperatures. The results of the analyses are used to create a diagram with non-dimensional axes with residual stress as a function of maximum thermal strain. The residual stresses are normalised with respect to the room temperature yield strength and the thermal strain normalised with respect to the room temperature yield strain. It is proposed that quench residual stresses can be estimated using this diagram irrespective of the quench conditions and bar diameter for steels. This is provided if there is no phase transformation during quenching. It is shown that if the normalised thermal strain is greater than about 3.6, the surface residual hoop and axial stresses are equal to the compressive room temperature yield strength, while the interior tensile stresses linearly increase (approximately) with thermal strain.
This article proposes a retrospective on experimental and numerical methods developed throughout the past century to solve the torsion problem in shafts, with particular emphasis on the determination of shear stress concentration factors in discontinuities of typical use in shaft design. This article, in particular, presents the theory and related solutions distinguishing between two classes of geometries: shafts with constant cross section and axisymmetric shafts with variable diameter. Emphasis is given to approaches based on physical analog methods and, in particular, those based on electrical analogies proposed since about 1925. Experimental methods based on structural physical models and numerical formulations are also reviewed, and a number of results from different approaches are collected and compared for two typical design case studies: a constant section shaft with a keyway and an axisymmetric shaft with a shouldered fillet.
An experimental and numerical study of the mechanical behaviour of cast iron during a thermomechanical fatigue is presented here. The cast iron specimens under investigation were made of austenitic ductile iron Ni-resist Type D-5S which is mostly used for exhaust manifolds and turbocharger housings. Elastoplastic and viscoplastic material parameters were determined from low cycle fatigue tests at different strain rates and thermomechanical fatigue tests, respectively, and then compared to material parameters previously gained by a combination of low cycle fatigue tests at a single strain rate and creep tests. These material parameters were then used to perform thermal and structural finite element analyses from which fatigue and creep damages on the cast iron were calculated. While damage predictions calculated here vary, they are comparable to experimental observations.
The increased desire to use advanced, high-strength steels for lightweight automotive structural components requires better understanding of thermo-mechanical behavior and appropriate experimental data for developing constitutive models. Thermo-mechanical studies are particularly important for understanding and optimizing hot-stamping processes which produce both complex and high-strength components. The experimental setup presented herein is capable of characterizing the thermo-mechanical behavior of such steels with strain rates up to approximately 1 s–1 and temperatures as high as 850 °C. The main parts of the apparatus are a high-speed camera, a load frame, and a box furnace. For the determination of strain, a simple image-processing program was developed. The strain was determined in three sections that span the entire gauge length of the specimen. Thus, the onset of localization could be more accurately determined. Stress versus strain data for various strain rates and temperatures are presented.
A technique to enhance the spatial resolution of typical fiber Bragg grating–based strain gauges has been experimentally verified in this study. Just analyzing the intensity of the reflection spectrum of a sampled fiber Bragg grating, its inner deformation profile has been obtained with a spatial resolution of
This work provides an exploratory investigation into the applicability of a two-parameter fracture mechanics approach based on the J-Q methodology to characterize fracture behavior in cracks located at geometrical discontinuities of pressure vessels submitted to pressurization and depressurization cycles. Numerical models in plane-strain condition were employed to characterize crack driving forces and constraint changes in a flawed structure subjected to shakedown. The material exhibits elastic–plastic behavior and nonlinear kinematic hardening following the Chaboche model. The results indicate that the application of cycles of loading exceeding elastic limits, but still below the allowable stress for design of pressure vessels, increases the crack driving force and decreases the constraint level. It is possible to conclude that the methodology based on J-Q is highly effective to characterize the fracture conditions in geometrical discontinuities of pressure vessels. A lower probability of unstable fracture may be assumed for ductile and high-toughness materials after few cycles of pressurization and depressurization are applied. However, due to the increase in the driving force, the crack may be more susceptible to a subcritical tearing. Assuming that the material toughness is high enough to avoid any ductile tearing during pressurization and depressurization cycles, the observed phenomena close to the crack tip may be compared to instability of strains when shakedown is not guaranteed.
This article presents a comprehensive piece of research work focused on the development, validation and application of finite element modelling capability for the prediction and optimization of robotic keyhole plasma arc welding of Ti-6Al-4V thin structures. Experimental and computational investigations were carried out to characterize, develop, optimize and validate various aspects of the finite element modelling. The experimental investigations cover the determination of welding parameter envelopes using a robotic welding cell and the measurements of thermal history, distortion, residual stress and weld pool profile. The computational investigations include the development and validation of finite element models as well as the development and validation of a fully automated welding sequence optimization tool using a genetic algorithm approach. The work provides useful guidance and generic methodologies for optimum design of thin and complex lightweight structures and has formed a basis for the development of a framework on structural integrity assessment and component lifing of thin structures fabricated by welding. The optimization tool has significant potential to be conveniently modified to suit other optimization objectives and/or welding processes.
In this article, a new method that combines finite element method with data mining techniques is proposed to obtain the mechanical properties of electrolytic tinplate. Using information provided by two simple and economic tests (hardness and spring-back), already used in industries to classify tinplate, yield stress and tensile parameters of a generic electrolytic tinplate can be estimated. Initially, a group of finite element models based on these simple tests were built and validated against experimental data. The validated finite element models were then used to investigate the effect of different thicknesses and electrolytic tinplate plastic hardening parameters. With the convergent results obtained from these finite element simulations, a database was generated with the new electrolytic tinplate properties. Various types of regression models (model trees, artificial neural networks and support vector machines) based on data mining techniques were used to obtain the yield stress and plastic hardening parameters from a generic sample of electrolytic tinplate. The accuracy of the results demonstrates that this new method may be used to economically predict yield stress and plastic hardening parameters of a generic electrolytic tinplate.
High-temperature components, for example turbochargers, are often subject to complex thermal and mechanical loading paths. Non-uniform temperature distribution and constraints by neighboring components result in complex timely varying stress and strain states during operation. The aim of this paper is to analyze inelastic behavior of a casting material Ni-resist D-5S in a wide stress, strain rate and temperature ranges. The material model including a constitutive equation for the inelastic strain rate tensor and a non-linear kinematic hardening rule is discussed. To calibrate the model, experimental databases from creep and low cycle fatigue tests are generated. They include creep curves for temperatures within the range 600–800 °C and stress levels from 10 to 150 MPa. The low cycle fatigue data collect a family of hysteresis loops for the strain rate of 10–3 1/s, the strain amplitude from 0.4% to 2% and temperature levels within the range 200–800 °C. For the verification of the model, simulations of the material behavior under uniaxial thermo-mechanical fatigue loading conditions are performed. The results for the stress response are compared with experimental data.
The finite element modelling of manufacturing processes often requires a large amount of large plastic strain flow stress data in order to represent the material of interest over a wide range of temperatures and strain rates. Compression data generated using a Gleeble thermo-mechanical simulator is difficult to interpret due to the complex temperature and strain fields, which exist within the specimen during the test. In this study, a non-linear optimisation process is presented, which includes a finite element model of the compression process to accurately determine the constants of a five-parameter Norton–Hoff material model. The optimisation process is first verified using a reduced three-parameter model and then the full five-parameter model using a known set of constants to produce the target data, from which the errors are assessed. Following this, the optimisation is performed using experimental target data starting from a set of constants derived from the test data using an initial least-squares fit and also an arbitrary starting point within the parameter space. The results of these tests yield coefficients differing by a maximum of less than 10% and significantly improve the representation of the flow stress of the material.
This article presents a novel measurement technique to measure local relative displacements between parts of large-scale structures. The measured deformations can be of significant importance for fracture analyses in many different types of structures in general and for adhesive connections in particular. The measurement of small local relative displacements in structures subjected to large global deformations is complex and hardly feasible with conventional measurement methods. Therefore, a small displacement measurement system has been devised. The small displacement measurement system is based on stereo photogrammetry and capable of measuring three-dimensional local displacements with a high degree of accuracy. In this article, the technique is used to measure local deformations in the vicinity of the adhesive trailing edge joint of a wind turbine rotor blade. The small displacement measurement system results correspond well with another independent measurement method.
In this article, we propose a direct approach to model the residual stress in glass due to ion exchange. Rather than employing the traditional thermal strain analogy approach in literature, the nominal residual strain distribution due to ion exchange is addressed with direct analysis of ion-exchange volume change first. Then, based on the principle of superposition, the residual stress in ion-exchanged glass is then formulated with a direct approach in the framework of elasticity, and a complete solution for residual stress distribution is obtained with consideration of the asymmetric ion molar concentration distribution. Finally, a simple example is provided to demonstrate the validity of the fundamental formulations proposed in this article.
This article presents an innovative testing machine for determining fracture toughness in double-notched cylindrical and prismatic test specimens loaded in shear over a wide range of applied strain rates and superimposed pressures. The equipment makes use of an electromagnetic actuator that is capable of accelerating the shearing punch against the specimens, with excellent repeatability and very precise control of the impact velocity, by means of the high pressure that is generated in a transient magnetic field produced by passing a pulse of electric current through a series of coils. Experiments performed in technically pure lead and aluminium AA1050-O give support to the presentation and allow understanding the influence of the loading rate and pressure on fracture toughness of ductile metals.
In this investigation, the influence of artificial finite adhesive defects with different shapes and sizes, characterized by (1) aspect ratios, a/b = 0.5, 1 and 1.5 (where a is transverse axis length of defect; b is longitudinal axis length of defect), (2) number of defects and (3) different locations, in the epoxy adhesive layer on the formability of adhesive-bonded blanks, is analysed. The deep drawing quality cold-rolled steel and stainless steel (SS 316L) sheets were used as base materials. The increase in aspect ratio of adhesive defect reduces the ductility of adhesive layer and thereby decreases the formability of adhesive-bonded blanks. This is due to the early failure of adhesive layer at the location of defect where strain is locally concentrated. The strain hardening exponent (n) of adhesive-bonded blanks has decreased with increase in aspect ratio of adhesive defect in all the regions of deformation. The limit strain of deep drawing quality and SS 316L sheets constituting adhesive-bonded blanks shows decrement with increase in aspect ratio of adhesive defect. It is postulated that the aspect ratio of the finite adhesive defect influences significantly the formability of adhesive-bonded blanks, but not shape of the finite adhesive defects. There is no considerable effect of number of adhesive defects and different locations of adhesive defects on the formability of adhesive-bonded blanks.
The measurement of residual stresses is of great importance in the glass industry. The analysis of residual stresses in the glass is usually carried out by photoelastic methods since the glass is a photoelastic material. This article considers the determination of membrane residual stresses of glass plates by digital photoelasticity. In particular, it presents a critical assessment concerning the automated methods based on gray-field polariscope, spectral content analysis, phase shifting, RGB photoelasticity, "test fringes" methods and "tint plate" method. These methods can effectively automate manual methods currently specified in some standards.
Although the understanding of volume change is of crucial importance to analyze and model the mechanical behavior of polymeric materials, it is highly understudied in the open literature. This article deals with the assessment of the volume change in polyetheretherketone when submitted to compressive loads. The volume change is measured by the end of mechanical tests before and after unloading. Therefore, the total (before unloading) and residual (after loading) volume changes are measured for strain rates ranging from 10–4 to 3000s–1 and temperatures ranging from + 133 to + 433 K, that is, –140 °C to + 160 °C. It is demonstrated that the total volume is almost constant in terms of the axial strain independent of strain rate and temperature. The residual volume slightly increases with increasing axial strain. This conclusion is obtained either by direct measurements or by a simplified model developed in this article. However, the volume change is softly affected by the specimen geometry.
In this article, a generalized cycle counting criterion applicable for both uniaxial and arbitrary multi-axial loading conditions is presented. This criterion consists of two parts: (1) an effective fatigue damage parameter definition in either stress or strain space and (2) a fatigue cycle definition corresponding to maximum damage possibly attained by the fatigue damage parameter within a given loading history. After discussing its mathematical and mechanics basis, we first provide a rigorous proof that the proposed generalized cycle counting criterion yields exactly the same results as the rainflow counting method under uniaxial variable amplitude loading conditions. Then, its applications in multi-axial fatigue are demonstrated by presenting a series of closed-form solutions of both the fatigue damage parameter and number of cycles for a general harmonic loading history of three independent traction stress components on a crack plane. The validity of the new generalized cycle counting criterion is demonstrated by its ability to correlate available fatigue test data in the literature. These new developments also provide a more refined physical and mechanics basis for the recently proposed path length–based cycle counting method developed by the same authors for performing cycle counting of variable amplitude multi-axial loading histories.
The main aim of this article is to propose some analytical and numerical expressions for evaluation of the critical value of the J-integral (Jcr) in plates weakened by blunt V-notches under Mode I loading for brittle or quasi-brittle materials. The critical J-integral is a material property in cracks. In notches, however, the specimen geometry also affects this parameter. In analytical expression, the relationship between J-integral and strain-energy density has been applied in order to evaluate the Jcr. The strain-energy density distribution over the semicircular arc of the notch (i.e. the parameter proposed in some previous articles) has also been used to derive a numerical equation for evaluation of the Jcr. The results have shown that the normalized Jcr (Jcr/JIC), that is, the ratio of the critical J-integral in notches to one in cracks, is a function of RC/ ratio, notch angle (2α), and Poisson’s ratio. The loading condition (bending or tensile loading), the ratio of the specimen width to the notch depth (w/a), and the notch acuity (a/) have negligible effect on the normalized Jcr, for constant values of other parameters. Good agreement was found in critical fracture load evaluated by means of the Jcr criterion (using the proposed equations) with experimental data taken from the literature for blunt V-notches under Mode I loading.
Material models are widely used in finite element codes for analysis of material deformations particularly at high strain rates and elevated temperatures. The problems such as necking and bulging limit the conventional test techniques to measure the stress–strain curves only up to small strains. This is while in some deformation processes, the strain can be greater than 1. In this study, steel shots of 6 mm in diameter are impacted on specimens at high impact velocities and at elevated temperatures using shot impact test. Strains up to 1.6 and strain rates up to about 4 x 106 s–1 are achieved in this study. The geometry of the crater created by the shot impact on the specimen is used for determination of the constants of Johnson–Cook material model. A combined experimental, numerical and optimization approach is used for determination of the constants. The experimental and numerical crater geometries coincide when the constants of material are chosen correctly. The selection of the constants is performed using an optimization technique such as genetic algorithm. The computed constants are verified by quasi-static tests. With this new technique, stress–strain curves are no longer needed to be obtained by experiment at high strain rates and elevated temperatures.
Fatigue crack growth tests have been carried out on two types of pre-cracked, hollow, Super CMV shaft specimens with transverse holes, under combined torsional and axial loading, from which crack growth patterns and crack growth data have been obtained. Experimental results show that the cracks were found to initially propagate under the Mode I condition on the planes of maximum tensile stress, and these then veered toward the planes of maximum shear stress and propagated under a mixture of Modes II and III patterns. A finite element approach is used to predict the fatigue crack growth, under the Mode I condition, in the shaft specimens tested at relatively low magnitudes of torque. A series of incremental finite element analyses, in conjunction with the use of Paris’ law, with different crack lengths and crack front profiles, are used to simulate the progressive fatigue crack growth process. The finite element predicted crack growth data are compared with the corresponding experimental data. Good agreement is obtained between the finite element predictions and the experimental results for relatively "short" crack growths, for crack lengths of up to about 1.25 mm. For the crack lengths greater than 1.25 mm, the finite element approach the fatigue crack growth rates and overpredicts the fatigue lives. The possible reasons for the difference between the predicted and tested results are also discussed.
Green gluing technology may have a large interest in wood industry. It allows energy saving, thus reducing costs. In order to fulfill requirements in relevant building codes and standards, these composite timbers have to present sufficient structural performance and shape stability. The drying step during the process of green gluing may lead to local strain and stress developments on the adhesive interface. These strain and stress developments could impact the shape stability of the product and induce joint failure. However, wood spatial microstructure may absorb these developments. It has to be noted that for an organic material such as wood, the measurement of hygromechanical properties must be done without any interactions between the material and the measurement system. In order to process in this way, an optical measurement system such as the digital image correlation has been used. Results have shown the local behavior of the interface during shrinkage of wood. The strains of the adhesive bond were calculated from the measurement by means of an inverse method.