In this work, a new model is proposed for predicting stress transients caused by strain path changes. The model is formulated in stress space, where a second order tensor, i.e., the microstructure ...stress deviator, is used to memorize and model the evolution history of the microstructure. Both its direction and magnitude are used to transiently distort the yield surface and to modify the work hardening. Orthogonal strain-path changes are handled by yield surface distortions, while Bauschinger effects are described by a kinematic hardening formulation. The model is calibrated to, and captures well, earlier published experiments for commercial pure aluminum, an extra deep drawing quality steel and a dual-phase steel. The proposed model describes qualitatively the response to double strain-path changes in low carbon steels. Efforts are made to design a relatively simple model as compared to the high complexity of the experiments, applying simple mathematical sub-models with straightforward interpretations and enabling a numerically stable implementation.
•A new distortional hardening model is proposed.•Microstructure deviator is used to distort yield surface and modify work hardening.•Transients occurring due to strain path changes in aluminum and steel are modeled.
•Implementation of a non-local GTN model to avoid spurious mesh dependency.•Applied to model damage evolution and crack propagation until complete fracture.•Validated against corresponding local GTN ...model.•Over-aggressive regularization is avoided by evaluating on current rather than initial configuration.
In this study, we follow the work of Tvergaard and Needleman (1995, 1997) and Needleman and Tvergaard (1998) and present the numerical implementation and initial applications of a non-local Gurson-Tvergaard-Needleman (GTN) model for explicit finite element (FE) analysis. The delocalization relates to the damage mechanism and is incorporated in terms of an integral condition on the rate of change of the porosity. To demonstrate the mesh independence during all stages of ductile damage and fracture, several material test specimens were simulated using different mesh sizes until full fracture occurred. For comparison purposes, the results are also obtained for the corresponding local GTN model in all cases. The effect of the material characteristic length on the ductile damage and fracture behavior and on the mesh sensitivity of the results is discussed. The numerical study shows that simulation results obtained in all stages of the ductile fracture process, including void growth, fracture initiation by coalescence and crack propagation all the way to a fully fractured specimen, are mesh independent for a certain mesh size ratio related to the material characteristic length, provided the non-local integral is evaluated on the current configuration. This ratio is unique for each individually simulated specimen as it depends on the spatial gradients of the porosity and the material parameters adopted for the problem at hand. It is shown that excessive averaging occurs at large deformations if the non-local integral is evaluated on the reference configuration, i.e., without updating the element interaction matrix resulting from the discretization of the non-local integral.
The stress-strain behavior of the aluminum alloy AA3103 subjected to single and double strain-path changes (SPCs) is studied experimentally. The experimental program includes compression-tension, ...tension-tension, rolling-tension and tension-rolling-tension tests. The considered AA3103 plate exhibits plastic anisotropy, a strong Bauschinger effect with hardening stagnation after strain reversal, cross-hardening and permanent softening after orthogonal SPCs in the tension-tension tests. However, when instead the orthogonal SPCs are obtained by rolling-tension tests, cross-softening is observed. The same behavior is seen in more complex tension-rolling-tension tests. Three state-of-the-art advanced plasticity models are used in an attempt to model the experimentally observed behavior. These models all account for plastic anisotropy and transient effects after SPCs, using a microstructure deviator tensor to describe a fading memory of the deformation history. While the models successfully describe the behavior after strain reversals, they fail to represent the behavior after orthogonal SPCs. It is concluded that the Schmitt angle, on which the current models depend, is not sufficient for a fundamental description of SPCs for the considered AA3103 alloy.
•An AlMn alloy that shows both strong reverse and orthogonal strain-path transients.•Attempts to calibrate state-of-the-art plasticity models are not satisfactory.•The Schmitt angle does not provide a fundamental description of the AA3103 alloy.
The occurrence of grain boundary precipitates was investigated with respect to the crystallographic orientation of the adjacent grains in extruded AA6110, AA6063 and AA6061 alloys brought to T6 ...temper. It was found that the requirement for grain boundary precipitate formation is for the adjacent grains to have Al directions or {100}Al planes parallel to the grain boundary plane. The highest density of grain boundary precipitates was present when this requirement was fulfilled by both adjacent grains.
In the present study, a hypoelastic–plastic formulation of porous crystal plasticity with a regularized version of Schmid’s law is proposed. The equation describing the effect of the voids on ...plasticity is modified to allow for an explicit analytical solution for the effective resolved shear stress. The regularized porous crystal plasticity model is implemented as a material model in a finite element code using the cutting plane algorithm. Fracture is described by element erosion at a critical porosity. The proposed model is used for two test cases of two- and three-dimensional polycrystals deformed in tension until full fracture is achieved. The simulations demonstrate the capability of the proposed model to account for the interaction between different modes of strain localization, such as shear bands and necking, and the initiation and propagation of ductile fracture in large scale polycrystal models with detailed grain description and realistic boundary conditions.
Commercially pure aluminum with random texture was prestrained either by rolling or by uniaxial compression, and then tested in uniaxial tension to study the transients in flow stress, work hardening ...and r-value induced by the strain-path change. New experimental results are reported on the variation of the r-value and the permanently reduced work hardening subsequent to the strain-path change. A continuum plasticity model was developed that can reproduce the observed behavior. The model applies a second-order “delayed pointer” tensor to represent the microstructural anisotropy and was implemented into the finite element software LS-DYNA. The model was calibrated to the experimental data, and a simulation of early strain localization subsequent to an orthogonal strain-path change was compared to strain fields measured by a digital image correlation technique.
•Experimental investigation of orthogonal and reverse strain-path changes in aluminum.•Model for transients after strain-path changes: Stress, work hardening and r-values.•Comparison of strain localization by digital image correlation and FEM model.
The strength differential (SD) effect, as reported in literature over the past decades, is a discrepancy between the axial stresses in compression and tension. This study investigates the SD effect ...in aluminum alloys using both experiments and numerical simulations. We present compressive and tensile tests of four aluminum alloys in several tempers with yield strengths varying from 27 MPa to 373 MPa: a total of thirteen different material configurations. The axial stresses measured in compression tests are significantly higher than corresponding tensile stresses for nearly all material configurations. In our tests, the SD effect generally increases with material strength, indicating that aluminum alloys are pressure sensitive. The physical mechanism responsible for the SD effect was not investigated in this paper, but a plasticity model based on the hypothesis that dislocation motion is affected by hydrostatic pressure, as put forth by several authors, gives an accurate description of the material behavior in compression and tension.
•Thirteen configurations of age hardened 6xxx aluminum alloys were tested.•The measured compressive and tensile axial stresses are different.•The strength differential increases with the strength of the material.•This is not attributed to geometrical changes or friction.•A Drucker-Prager model calibrated from results from literature captures this behavior.
The mechanical response of dual phase (DP) steel exhibits a complex dependence on the microstructure. The chemical composition and microstructure characteristics of the phases have significant ...effects on the contrast between the response of the phases, which affects, not only the strength and ductility, but also the anisotropic response of DP steel under strain path changes. In this work, extended dislocation-based models of the ferrite and martensite phases of DP steel are proposed and used in a finite element based representative volume element approach to account for the contrast between the local response of the phases. The flow stress of each phase is computed as a function of the amount of substitutional and interstitial solute elements and the microstructural characteristics of the phase. Particular attention is paid to the phase model of the martensite phase. The model parameter controlling the storage of dislocations is related to the carbon content, which appears to be the most important parameter affecting the strength of martensite and its contrast with the local response of the ferrite phase. The model predicts a significant effect of the contrast between the local responses of the phases and the microstructure characteristics of each phase on the yield locus after prestraining and on the stress–strain behaviour after strain path change, i.e., forward-reverse shear loading and cyclic uniaxial tension–compression loading.
In this paper, we investigate the possibility of predicting ductile fracture of pipeline steel by using the Gurson–Tvergaard–Needleman (GTN) model where the onset of void coalescence is determined ...based on in situ bifurcation analyses. To this end, three variants of the GTN model, one of which includes in situ bifurcation, are calibrated for a pipeline steel grade X65 using uniaxial and notch tension tests. Then plane-strain tension tests and Kahn tear tests of the same material are used for assessment of the credibility of the three models. Explicit finite element simulations are carried out for all tests using the three variants of the GTN model, and the results are compared to the experimental data. The capability of the simulation models to capture onset of fracture and crack propagation in the pipeline steel is evaluated. It is found that the use of in situ bifurcation as a criterion for onset of void coalescence in each element makes the GTN model easier to calibrate with less free parameters, all the while obtaining similar or even better predictions as other widely used formulations of the GTN model over a wide range of different stress states.
The influence of microstructure on plasticity and fracture of three 6000-series aluminum alloys is studied with emphasis on the anisotropy caused by the extrusion process. Tension tests on smooth and ...notched specimens are performed in different directions with respect to the extrusion direction, where the stress and strain to fracture are based on local measurements inside the neck or notch. The microstructure of the alloys, i.e., grain structure, crystallographic texture and size distribution of constituent particles, is characterized and used to explain the experimental findings. The experiments show considerable differences in the directional variation of the yield stress, the plastic flow, the work hardening, and the failure strain between alloys exhibiting recrystallization texture and deformation texture. The alloys with recrystallized microstructure exhibited substantial anisotropic work hardening caused by texture evolution and a stronger notch sensitivity of the failure strain than the alloy with deformed, non-recrystallized microstructure. Comparisons are made with previous experiments on the same alloys in the cast and homogenized condition, and the effects of the microstructural changes caused by the extrusion process on the macroscopic response are discussed.
PDF
