Zhiliang Zhang

A complete Gurson model approach for ductile fracture

Abstract Recently, a complete Gurson model has been introduced by the authors. The complete Gurson model is a combination of the modified Gurson model which deals with microvoid nucleation and growth, and a physical microvoid coalescence criterion based on the plastic limit load model by Thomason. By comparing finite element cell modeling analyses, the complete Gurson model is accurate for both non-hardening and hardening materials. One attractive feature of the complete Gurson model is that material ductile failure is exclusively linked to the microvoid nucleation parameter, and the nucleation parameter in many cases can be determined without metallurgical examinations. Furthermore, the so-called critical void volume fraction fc, has been eliminated from material constants. In this paper, two simple microvoid nucleation models for modeling ductile fracture are discussed, and a method which applies multitension specimens including both smooth and notched cylindrical specimens for determining the microvoid nucleation parameter is introduced. Once the microvoid nucleation parameter has been determined from the tension specimens, the characteristic length parameter which describes the stress/strain gradient effect can be fitted from fracture mechanics tests. Material ductile crack resistance behavior is then a function of the microvoid nucleation parameter, the length parameter and the specimen geometry. For modified boundary layer models, it has been found that the crack resistance curves can be normalized by the T stress, and the T stress can be possibly taken as the geometry controlling parameter for ductile crack growth.

Determining material true stress-strain curve from tensile specimens with rectangular cross-section

Abstract The uniaxial true stress logarithmic strain curve for a thick section can be determined from the load–diameter reduction record of a round tensile specimen. The correction of the true stress for necking can be performed by using the well-known Bridgman equation. For thin sections, it is more practical to use specimens with rectangular cross-section. However, there is no established method to determine the complete true stress–logarithmic strain relation from a rectangular specimen. In this paper, an extensive three-dimensional numerical study has been carried out on the diffuse necking behaviour of tensile specimens made of isotropic materials with rectangular cross-section, and an approximate relation is established between the area reduction of the minimum cross-section and the measured thickness reduction. It is found that the area reduction can be normalized by the uniaxial strain at maximum load which represents the material hardening and also the section aspect ratio. Furthermore, for the same material, specimens with different aspect ratio give exactly the same true average stress–logarithmic strain curve. This finding implies that Bridgmans correction can still be used for necking correction of the true average stress obtained from rectangular specimens. Based on this finding, a method for determining the true stress–logarithmic strain relation from the load–thickness reduction curve of specimens with rectangular cross-section is proposed.

A new failure criterion for the Gurson-Tvergaard dilational constitutive model

In the Gurson-Tvergaard model a failure criterion has to be used to signify the void coalescence. In the literature, a constant critical void volume fraction criterion has been widely used. However, it is questionable whether the critical void volume fraction is a material constant and, furthermore, it is also difficult in practice to determine the ‘constant’. By modifying Thomasons plastic limit-load model, a new failure criterion which is fully compatible with the Gurson-Tvergaard model, is presented in this study. In the present criterion, the void coalescence failure mechanism by internal necking has been considered and the material failure is a natural result of the development of dual constitutive, stable and unstable, responses. In practical application of the present criterion, no critical void volume fraction needs to be pre-determined either numerically or experimentally. Furthermore, according to the new criterion, the void volume fraction corresponding to void coalescence is not a material constant, rather a function of stress triaxiality. The predictions using the present criterion have been compared with the finite element results by Koplik and Needleman, and very good agreement is observed. The potential advantage of this criterion and other related issues are discussed.

Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models

Abstract In order to preserve the quadratic rate of asymptotic convergence, for the widely-used iterative schemes based on Newtons method, it is crucial to ensure consistency between the tangent moduli and the integration algorithm. By exact linearization of the algorithm and decomposition of the stresses into hydrostatic and deviatoric parts, a method is presented whereby an explicit expression for the tangent moduli consistent with a closest point return mapping algorithm may be developed for generalized pressure-dependent elastolasticity models. One significant advantage of this method is that no matrix inversion is necessary in the consistent tangent moduli expression. For classical J 2 elastoplasticity associated with an isotropic hardening rule problem, the present consistent tangent moduli coincide with consistent tangent moduli given by others. Application is made to fixed Gurson-based model as well as Gurson-based model. The excellent convergence performance of the consistent tangent moduli is illustrated in numerical experiments.

Two-parameter characterization of the near-tip stress fields for a bi-material elastic-plastic interface crack

A particular case of interface cracks is considered. The materials at each side of the interface are assumed to have different yield strength and plastic strain hardening exponent, while elastic properties are identical. The problem is considered to be a relevant idealization of a crack at the fusion line in a weldment. A systematic investigation of the mismatch effect in this bi-material plane strain mode I dominating interface crack has been performed by finite strain finite element analyses. Results for loading causing small scale yielding at the crack tip are described. It is concluded that the near-tip stress field in the forward sector can be separated, at least approximately, into two parts. The first part is characterized by the homogeneous small scale yielding field controlled by J for one of the interface materials, the reference material. The second part which influences the absolute value of stresses at the crack tip and measures the deviation of the fields from the first part can be characterized by a mismatch constraint parameter M. Results have indicated that the second part is a very weak function of distance from the crack tip in the forward sector, and the angular distribution of the second part is only a function of the plastic hardening property of the reference material.

Role of Five-fold Twin Boundary on the Enhanced Mechanical Properties of fcc Fe Nanowires

The role of 5-fold twin boundary on the structural and mechanical properties of fcc Fe nanowire under tension is explored by classical molecular dynamics. Twin-stabilized fcc nanowire with various diameters (6-24 nm) are examined by tension tests at several temperatures ranging from 0.01 to 1100 K. Significant increase in the Youngs modulus of the smaller nanowires is revealed to originate from the central area of quinquefoliolate-like stress-distribution over the 5-fold twin, rather than from the surface tension that is often considered as the main source of such size-effects found in nanostructures. Because of the excess compressive stress caused by crossing twin-boundaries, the atoms in the center behave stiffer than those in bulk and even expand laterally under axial tension, providing locally negative Poissons ratio. The yield strength of nanowire is also enhanced by the twin boundary that suppresses dislocation nucleation within a fcc twin-domain; therefore, the plasticity of nanowire is initiated by strain-induced fcc→bcc phase transformation that destroys the twin structure. After the yield, the nucleated bcc phase immediately spreads to the entire area, and forms a multigrain structure to realize ductile deformation followed by necking. As temperature elevated close to the critical temperature between bcc and fcc phases, the increased stability of fcc phase competes with the phase transformation under tension, and hence dislocation nucleations in fcc phase are observed exclusively at the highest temperature in our study.

On the accuracies of numerical integration algorithms for Gurson-based pressure-dependent elastoplastic constitutive models

Abstract A class of generalized mid-point algorithms for pressure-dependent elastoplastic models is formulated in the paper. The accuracies of the formulated generalized mid-point algorithms including the Euler backward algorithm and the one-step Euler forward algorithm are systematically analyzed against the exact solution for Gurson-based pressure-dependent elastoplastic model. The accuracies of the algorithms are assessed by means of iso-error maps. Results show that the formulated generalized mid-point algorithms are reasonably accurate in both small and large increment steps. It is found that in all the cases considered, the maximum errors in the presence of volumetric strain increments are less than those without volumetric strain increments. When the deviatoric strain increments are given in the radial direction, the true mid-point algorithm is the most accurate one. Furthermore, the optimal value α of the generalized mid-point algorithms, in terms of maximum errors, is observed between 0.5 and 1. For both small and large increment steps, the one-step Euler forward algorithm gives the worst accuracy.

Effects of crack size and weld metal mismatch on the has cleavage toughness of wide plates

Abstract The heat affect zone (HAZ) is in many cases considered to be the most critical part of a weldment. In this paper, the effect of crack size and weld metal mismatch on the HAZ cleavage toughness of wide plate specimens with X-groove has been investigated by the J-Q-M theories and a simple micromechanism for cleavage fracture. Two crack sizes have been studied ( a w = 0.1 and 0.3). In the analyses, the HAZ yield strength is assumed to be higher than the base metal. For each crack size, weld metal local overmatch and local evenmatch with respect to the HAZ are considered. For a given global strain, the results indicate that weld metal overmatch and evenmatch yield the same crack tip loading in terms of J-integral for a w = 0.3 . For a w = 0.1 , overmatch gives lower crack tip loading than evenmatch. For a given crack tip loading, weld metal local evenmatch in general results in less effective crack tip loading than the overmatch. Overmatch is detrimental to HAZ toughness, but this detrimental effect becomes less significant when the crack size decreases.

A study on determining true stress–strain curve for anisotropic materials with rectangular tensile bars

Recently, a method has been proposed for determining material true stress–strain curve with rectangular tensile bars up to localized necking. In the proposed method, material true stress–strain curve can be directly calculated from the load versus thickness reduction (at the minimum cross-section) curve. The method was established based on the finite element (FE) analysis for isotropic materials. In this study, this method has been extended for materials with isotropic elastic properties but anisotropic plastic properties. Two cases, transverse anisotropy and planar anisotropy, have been considered. Hill’s anisotropic material model implemented in abaqus was applied for the study. More than 30 three-dimensional FE analyses of rectangular specimens with different anisotropy value, hardening exponent and cross-section aspect ratio have been carried out. It is shown that the relation between thickness reduction and total area reduction of a given cross-section is influenced by material plastic anisotropy. It is, however, found that the anisotropic effect on the thickness–area reduction relation can be normalized by the width to thickness strain increment ratio r, and a modified thickness–area reduction relation is proposed and numerically and experimentally verified. One practical problem in tensile test is that it is difficult to predict the necking location. In this regard, a study on the sensitivity of initial notch geometry has been carried out. It is found that for a fixed initial notch radius, the percentage of error is approximately equal to the percentage of initial width reduction. The accuracy of using large initial width reduction can be improved by using large notch radius.

Studies on the ductility predictions by different local failure criteria

Abstract It is well known that the ductile fracture of metals has frequently been observed to result from the growth and coalescence of microscopic voids. Correspondingly, local approach methodologies have been developed in the modelling of ductile fracture. Three local ductile fracture criteria, a critical void volume fraction criterion based on a Gurson-type constitutive relation, a critical void growth criterion based on Rice-Tracey void growth equations, and Thomasons plastic limit-load criterion, have been studied and examined against the predictions of ductility with respect to stress triaxiality. A calibration for the predictions of the plastic limit-load criterion has been made, which yields a modification to the criterion to give more realistic predictions at low stress triaxiality than the original criterion. Various comparisons of the criteria have been made. It has been found that there are considerable differences in the predictions by the three criteria. Finally, a method has been introduced which can correlate the predictions well using dual dilational constitutive models.