An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

近场动力学研究进展与岩石破裂过程模拟

近场动力学（Peridynamics,PD）作为一种新兴的非局部性理论,在非连续处不需要任何处理,能够很好表述模型从连续到非连续的过程。首先,在PD基本理论简介的基础上,系统回顾了PD的国内外研究现状。其次,采用键型PD理论对非均匀性的圆孔岩板单轴拉伸破裂过程进行了二维数值模拟,采用态型PD理论对单轴、常规三轴以及真三轴等不同压缩条件下的岩石破裂过程进行了三维数值模拟,并以加拿大Mine-by隧洞为例对现场岩体破裂过程进行了模拟,结果表明PD在岩石破裂过程模拟上具有较强适用性。最后,指出当前PD在岩石破裂过程模拟中存在的主要问题和未来值得开展的若干研究课题。     

Application of Laser Deposition to Mechanical Characterization of Advanced High Strength Steels Subject to Non-Proportional Loading

Background

Characterization of hardening and fracture limits of advanced high strength steels (AHSSs) undergoing strain path changes (SPCs) are particularly challenging for plane strain condition, which commonly occurs in sheet metal forming. There is a need for a simple, engineering-friendly method to characterize materials subjected to complex loading paths that mimic stress conditions in actual forming processes.

Objective

Experimental additive manufacturing techniques have been applied to reinforce AHSS specimens subjected to SPCs in order to broaden capabilities for characterizing hardening behavior and fracture limits.

Methods

Hardening curves subject to SPCs (e.g. uniaxial tension or equi-biaxial tension followed by plane strain) have been obtained with a programmable biaxial tensile testing system using cruciform-shaped specimens with load-bearing arms reinforced by laser deposition. A notched specimen selectively reinforced by laser deposition was newly designed to characterize fracture limits subjected to SPCs ending with plane strain condition.

Results

Complex loading histories were successfully enabled by applying laser deposition technology. Results show that both hardening behavior and fracture limits of a TRIP-assisted steel and a dual-phase steel are dependent on loading history.

Conclusions

It appears that the laser deposition technique can be used for material characterization under specific SPCs. Hardening behavior of AHSSs under SPCs ending with plane strain is quite different from traditional uniaxial tension-uniaxial compression tests. For materials sensitive to SPCs, multi-step forming can be a great option to reach the targeted forming shape.

     

Anisotropic plasticity model coupled with Lode angle dependent strain-induced transformation kinetics law

A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations are embedded in the framework of finite strain isothermal rate-independent anisotropic plasticity. Experimental data for an anisotropic austenitic stainless steel 301LN is presented for uniaxial tension, uniaxial compression, transverse plane strain tension and pure shear. The model parameters are identified using a combined analytical–numerical approach. Numerical simulations are performed of all calibration experiments and excellent agreement is observed. Moreover, we make use of experimental data from ten combined tension and shear experiments to validate the proposed constitutive model. In addition, punch and notched tension tests are performed to evaluate the model performance in structural applications with heterogeneous stress and strain fields.     

Prediction of plane strain fracture of AHSS sheets with post-initiation softening

In this investigation, the three-parameter Modified Mohr–Coulomb (MMC) fracture model and the determination of the material parameters are briefly described. The formulation of the post-initiation behavior is proposed by defining both the explicit softening law and the incremental damage evolution law. As opposed to the existing attempts to simulate slant fracture with material weakening before crack formation, softening is assumed to occur only in the post-initiation range. The justification of this assumption can be provided by the interrupted fracture tests, for example, Spencer et al. (2002).Element deletion with a gradual loss of strength is used to simulate crack propagation after fracture initiation. The main emphasis of the paper is the numerical prediction of slant fracture which is almost always observed in thin sheets. For that purpose, VUMAT subroutines of ABAQUS are coded with post-initiation behavior for both shell elements and plane strain elements. Fracture of flat-grooved tensile specimens cut from advanced high strength steel (AHSS) sheets are simulated by 2D plane strain element and shell element models.     

Evaluation of the VDA 238–100 Tight Radius Bend Test for Plane Strain Fracture Characterization of Automotive Sheet Metals

Accurate characterization of the fracture limit in plane strain tension of automotive sheet metals is critical for the design and crash performance of structural components. Plane strain bending using the VDA 238–100 V-bend test has potential for proportional fracture characterization by avoiding a tensile instability. The VDA 238–100 V-bend test was evaluated using DIC strain measurement to characterize the plane strain fracture limit under proportional plane stress loading and to evaluate the effect of the VDA pre-straining methodology for ductile alloys upon the material response. The load-based failure criterion of the V-bend test was evaluated with DIC to monitor the development of surface cracking. The influence of the non-linear strain path imposed by the pre-straining procedure for ductile materials was then evaluated for three automotive alloys: an advanced high strength dual phase steel, DP1180, a rare-earth magnesium, ZEK100, and an AA5182 aluminum. A fracture criterion based on the load threshold was reasonable for the three alloys considered. Pre-straining in uniaxial tension prior to plane strain bending affected each alloy differently. The DP1180 was not affected by the non-linear strain path whereas the cumulative equivalent strain for the AA5182 and ZEK100 increased by strains of 0.07 and 0.05 strain, respectively. The non-linear strain path within the VDA pre-straining methodology creates ambiguity in comparing the fracture limits of different materials. The plane strain fracture limit for proportional loading can be readily obtained in the V-bend test with DIC strain measurement.

     

Large deformation extensional rheology of bread dough

The stress–strain curves of bread dough were derived under uniaxial compression, uniaxial tension and equi-biaxial tension loading conditions. In uniaxial compression, a lubricant was used to eliminate frictional effects between the loading platens and the sample. In uniaxial tension, cylindrical samples with thin flat discs at both ends (‘I’ samples) were tested. The discs at both ends were allowed to air-dry and were subsequently glued onto the loading platens. In equi-biaxial tension, a thin disc of dough was inflated into a bubble using pressurised air. The thickness at the top of the bubble was measured by shining a light through the walls of the bubble and recording the change in light intensity as the wall becomes thinner. All methods ensured that uniform deformation was obtained. Stress and strain were accurately evaluated using image analysis techniques. The tests were performed at various strain rates and speeds that defined the time dependence of the material. A non-linear viscoelastic model based on the Prony series and Van der Waals hyperelasticity was used to predict all test data. The model had a total of five material parameters and two time constants, which were set to represent the actual time scales of the experiments. A reasonable agreement between the experimental data and the chosen material model was observed.     

Atomistic measure of the strength of MgO nanorods

Molecular dynamics (MD) simulations were employed to study material response of MgO nanorod subjected to uniaxial tension loading. The simulations show in detail the atomic-scale mechanism of the deformation and failure process during tension. The effects of strain rate, system size and environment temperature on the strength of MgO nanorods are observed. It is found that the materials appear more ductile at lower strain rate, and the tensile strength of the nanorod decreases as the diameter of system cross-section decreases and as temperature increases.     

Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals

A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains.     

Coupled experiments and simulations of microstructural damage in wood

In this paper, we explore ways to couple experimental measurements with the numerical simulations of the mechanical properties of wood. For our numerical simulations, we have adopted a lattice approach, where wood fibers or bundles of wood fibers are modeled as discrete structural elements connected by a lattice of spring elements. Element strength and stiffness properties are determined from bulk material properties. Damage is represented by broken lattice elements, which cause both stiffness and strength degradation. The modeling approach was applied to small specimens of spruce subjected to transverse uniaxial tension, and mode I transverse splitting. The model was found to be good at predicting the load-deformation response of both notched and unnotched specimens, including the post-peak softening response. In addition, the damage patterns predicted by the model are consistent with those observed in the experiments.     

Numerical analysis of cracked inelastic shells with large displacements or mixed mode loading

The trend in higher utilization of structural materials leads to a need for accurate numerical tools for reliable predictions of structural response. In some instances both material and geometrical nonlinearities are allowed for, typically in assessments of structural collapse or residual strength in damaged conditions. Dynamically loaded structures are prone to fatigue cracking; this has to be accounted for when computing nonlinear structural response. The present study addresses the performance of cracked inelastic shells with out-of-plane displacement not negligible compared to shell thickness. This situation leads to membrane force effects in the shell. Hence, a cracked part of the shell will be subjected to a nonproportional history of bending moment and membrane force, and e.g. fracture mechanics parameters (J-integral ) are affected. A Mindlin shell finite element based nonlinear program is developed and utilized herein. The cracked parts are accounted for by means of inelastic line spring elements. These elements also account for possible mode II deformations.     

A combined experimental–numerical investigation of ductile fracture in bending of a class of ferritic–martensitic steel

We present a combined experimental–numerical study on fracture initiation at the convex surface and its propagation during bending of a class of ferritic–martensitic steel. On the experimental side, so-called free bending experiments are conducted on DP1000 steel sheets until fracture, realizing optical and scanning electron microscopy analyses on the post mortem specimens for fracture characterization. A blended Mode I – Mode II fracture pattern, which is driven by cavitation at non-metallic inclusions as well as martensitic islands and resultant softening-based intense strain localization, is observed. Phenomena like crack zig-zagging and crack alternation at the bend apex along the bending axis are introduced and discussed. On the numerical side, based on this physical motivation, the process is simulated in 2D plane strain and 3D, using Gurson’s dilatant plasticity model with a recent shear modification, strain-based void nucleation, and coalescence effects. The effect of certain material parameters (initial porosity, damage at coalescence and failure, shear modification term, etc.), plane strain constraint and mesh size on the localization and the fracture behavior are investigated in detail.     

Combined grain size, strain rate and loading condition effects on mechanical behavior of nanocrystalline Cu under high strain rates

Molecular dynamics simulations of nanocrys-talline Cu with average grain sizes of 3.1 nm, 6.2 nm, 12.4 nm and 18.6 nm under uniaxial strain and stress tension at strain rates of 10 8 s 1 , 10 9 s 1 and 10 10 s 1 are performed to study the combined grain size, strain rate and loading condition effects on mechanical properties. It is found that the strength of nanocrystalline Cu increases as grain size increases regardless of loading condition. Both the strength and ductility of nanocrystalline Cu increase with strain rate except that there is no monotonic relation between the strength and strain rate for specimens under uniaxial strain loading. Moreover, the strength and ductility of specimens under uniaxial strain loading are lower than those under uniaxial stress loading. The nucleation of voids at grain boundaries and their subsequent growth characterize the failure of specimens under uniaxial strain loading, while grain boundary sliding and necking dominate the failure of specimens under uniaxial stress loading. The rate dependent strength is mainly caused by the dynamic wave effect that limits dislocation motion, while combined twinning and slipping mechanism makes the material more ductile at higher strain rates.     

45钢的J-C损伤失效参量研究

为了在结构碰撞效应的有限元分析中描述材料行为,通过开展45钢在不同应力状态和温度下的准静态材料力学性能实验及拉伸SHB实验,考察了应力状态三轴度、温度和应变率对材料失效应变的影响。由实验数据得到了Johnson-Cook失效模型参量,并通过出现失效的Taylor撞击实验和数值模拟进行了一定的验证,表明模型描述与实验结果的趋势一致。     

Effects of stress invariants and reverse loading on ductile fracture initiation

Recent research studies on ductile fracture of metals have shown that the ductile fracture initiation is significantly affected by the stress state. In this study, the effects of the stress invariants as well as the effect of the reverse loading on ductile fracture are considered. To estimate the reduction of load carrying capacity and ductile fracture initiation, a scalar damage expression is proposed. This scalar damage is a function of the accumulated plastic strain, the first stress invariant and the Lode angle. To incorporate the effect of the reverse loading, the accumulated plastic strain is divided into the tension and compression components and each component has a different weight coefficient. For evaluating the plastic deformation until fracture initiation, the proposed damage function is coupled with the cyclic plasticity model which is affected by all of the stress invariants and pervious plastic deformation history.For verification and evaluation of this damage-plasticity constitutive equation a series of experimental tests are conducted on high-strength steel, DIN 1.6959. In addition finite element simulations are carried out including the integration of the constitutive equations using the modified return mapping algorithm. The modeling results show good agreement with experimental results.     

Effects of the strain-hardening exponent on two-parameter characterizations of surface-cracks under large-scale yielding

The influence of strain hardening exponent on two-parameter J-Q near tip opening stress field characterization with modified boundary layer formulation and the corresponding validity limits are explored in detail. Finite element simulations of surface cracked plates under uniaxial tension are implemented for loads exceeding net-section yield. The results from this study provide numerical methodology for limit analysis and demonstrate the strong material dependencies of fracture parameterization under large scale yielding. Sufficient strain hardening is shown to be necessary to maintain J-Q predicted fields when plastic flow progresses through the remaining ligament. Lower strain hardening amplifies constraint loss due to stress redistribution in the plastic zone and increases the ratio of tip deformation to J. The onset of plastic collapse is marked by shape change and/or rapid relaxation of tip fields compared to those predicted by MBL solutions and thus defining the limits of J-Q dominance. A radially independent Q-parameter cannot be evaluated for the low strain hardening material at larger deformations within a range where both cleavage and ductile fracture mechanisms are present. The geometric deformation limit of near tip stress field characterization is shown to be directly proportional to the level of stress the material is capable of carrying within the plastic zone. Accounting for the strain hardening of a material provides a more adjusted and less conservative limit methodology compared to those generalized by the yield strength alone. Results from this study are of relevance to establishing testing standards for surface cracked tensile geometries.     

A new quasi-continuum constitutive model for crack growth in an isotropic solid

A new quasi-continuum constitutive model is established based on the randomized cohesive bonds model proposed by Gao and Klein (1998). This model bridges the microscopic discrete constitution characters and the macroscopic mechanical properties of material. In the presented constitutive model, both the bond stretch energy potential and the rotation energy potential are considered, which makes the presented constitutive model applicable to different Poisson-ratio and Young's modulus materials. By establishing a phenomenological bond stiffness function according to the complete stress–strain relationship of uniaxial tension test, the fracture criterion is directly incorporated into the constitutive model. The method requires no external fracture criterion when simulating fracture initiation and propagation, which brings convenience in the numerical simulation. At last, the presented constitutive model is applied to an example of crack growth in an isotropic solid.     

Stress–strain relations for hydrogels under multiaxial deformation

Constitutive equations are derived for the elastic response of swollen elastomers and hydrogels under an arbitrary deformation with finite strains. An expression is developed for the free energy density of a polymer network based on the Flory concept of flexible chains with constrained junctions and solvent-dependent reference configuration. The importance of introduction of a reference configuration evolving under swelling is confirmed by the analysis of experimental data on nanocomposite hydrogels subjected to swelling and drying. Adjustable parameters in the stress–strain relations are found by fitting observations on swollen elastomers, chemical gels (linked by covalent bonds and sliding cross-links), and physical gels under uniaxial stretching, equi-biaxial tension, and pure shear. Good agreement is demonstrated between the observations and results of numerical simulation. A pronounced difference is revealed between the effect of solvent content on elastic moduli of chemical and physical gels.     

Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension

This paper deals with the evolution of inhomogeneous deformation in shape memory alloy strips and mild steel strips under uniaxial tension. New experiments on NiTi strips, which initially are in an austenitic phase, show that at a critical stress level martensite nucleates in sharp bands inclined at 55° to the axis of loading. Under prescribed end displacement martensite subsequently spreads either by steady-state propagation of inclined transition fronts or via a criss-cross pattern of finger-like features. Similar events have been reported in the literature regarding the evolution of Lüders bands in fine grained steel strips and wires. The similarity of macroscopic events, despite the different mechanisms of instability at the micro-level, prompted us to approximate the material behavior as a finitely deforming elasto-plastic solid with a trilinear up-down-up nominal stress-strain response. Two such stress-strain responses were used in finite element simulations of strip tension tests. In the first the true stress-strain response maintains its stability and in the second the intermediate branch has a negative slope. While both material models produced inhomogeneous deformations with features similar to those of the experiments, the larger initiation peak associated with the second gave results which closely resembled specific experiments. The numerical simulations confirmed that the evolution of events seen in experiments on SMAs and mild steels is strongly influenced by overall geometric (structural) effects. Furthermore, the success of this simple continuum constitutive model strongly suggests that continuum level events remain dominant players in such fine grained materials.