J.X. Liu

Finite element modelling of superplastic-like forming using a dislocation density-based model for AA5083

Superplastic-like forming is a newly improved sheet forming process that combines the mechanical pre-forming (also called hot drawing) with gas-driven blow forming (gas forming). Non-superplastic grade aluminium alloy 5083 (AA5083) was successfully formed using this process. In this paper, a physical-based material model with dislocation density and vacancy concentration as intrinsic foundations was employed. The model describes the overall flow stress evolution of AA5083 from ambient temperature up to 550??C and strain rates from 10?4 up to 10?1?s?1. Experimental data in the form of stress?strain curves were used for the calibration of the model. The calibrated material model was implemented into simulation to model the macroscopic forming process. Hereby, finite element modelling (FEM) was used to estimate the optimum strain-rate forming path, and experiments were used to validate the model. In addition, the strain-rate controlled forming was conducted for the purpose of maintaining the gas forming with an average strain rate of 2???10?3?s?1. The predicted necking areas closely approximate the localized thinning observed in the part. Strain rate gradients as a result of geometric effects were considered to be the main reason accounting for thinning and plastic straining, which were demonstrated during hot drawing and gas forming by simulations.

On the Load–Unload (L–U) and Force–Release (F–R) Algorithms for Simulating Brittle Fracture Processes via Lattice Models

General summaries on the load–unload and force–release methods indicate that the two methods are efficient for different-charactered quasi-static failures; therefore, it is important to choose the right one for different applications. Then we take, as an example, the case where the release of the ruptured elements internal force is infinitely slower than the relaxation of the lattice system and analyze why the force–release method works better than the load–unload method in this particular case. Different trial deformation fields are used by them to track the next equilibrium state. Force–release method ensures that the deformation throughout the whole failure process coincides exactly with the controlled-displacement boundary conditions and we utilize the ‘left modulus’ concept to prove that this method satisfies the energetic evolution in the force–displacement diagram; both of which are not satisfied by the load–unload method. To illustrate that the force–release method is not just another form of the load–unload method, a tensile test on a specifically designed system is analyzed to further compare the above two methods, showing that their predicted sequences of elemental failures can be different. In closing, we simulate the uniaxial tensile test on a beam lattice system by the load–unload and force–release methods and exploit the details of the resulting fracture processes.

A variational constitutive model for the distribution and interactions of multi-sized voids

The evolution of defects or voids, generally recognized as the basic failure mechanism in most metals and alloys, has been intensively studied. Most investigations have been limited to spatially periodic cases with non-random distributions of the radii of the voids. In this study, we use a new form of the incompressibility of the matrix to propose the formula for the volumetric plastic energy of a void inside a porous medium. As a consequence, we are able to account for the weakening effect of the surrounding voids and to propose a general model for the distribution and interactions of multi-sized voids. We found that the single parameter in classical Gurson-type models, namely void volume fraction is not sufficient for the model. The relative growth rates of voids of different sizes, which can in principle be obtained through physical or numerical experiments, are required. To demonstrate the feasibility of the model, we analyze two cases. The first case represents exactly the same assumption hidden in the classical Gurson’s model, while the second embodies the competitive mechanism due to void size differences despite in a much simpler manner than the general case. Coalescence is implemented by allowing an accelerated void growth after an empirical critical porosity in a way that is the same as the Gurson–Tvergaard–Needleman model. The constitutive model presented here is validated through good agreements with experimental data. Its capacity for reproducing realistic failure patterns is shown by simulating a tensile test on a notched round bar.

A quasi-static algorithm that includes effects of characteristic time scales for simulating failures in brittle materials

When the brittle heterogeneous material is simulated via lattice models, the quasi-static failure depends on the relative magnitudes of T elem , the characteristic releasing time of the internal forces of the broken elements and T lattice , the characteristic relaxation time of the lattice, both of which are infinitesimal compared with T load , the characteristic loading period. The load–unload (L–U) method is used for one extreme, Telem ≪ Tlattice, whereas the force–release (F–R) method is used for the other, Telem ≫ Tlattice. For cases between the above two extremes, we develop a new algorithm by combining the L–U and the F–R trial displacement fields to construct the new trial field. As a result, our algorithm includes both L–U and F–R failure characteristics, which allows us to observe the influence of the ratio of T elem to T lattice by adjusting their contributions in the trial displacement field. Therefore, the material dependence of the snap-back instabilities is implemented by introducing one snap-back parameter γ. Although in principle catastrophic failures can hardly be predicted accurately without knowing all microstructural information, effects of γ can be captured by numerical simulations conducted on samples with exactly the same microstructure but different γs. Such a same-specimen-based study shows how the lattice behaves along with the changing ratio of the L–U and F–R components.

Constitutive modeling of rate dependence and microinertia effects in porous-plastic materials with multi-sized voids (MSVs)

Micro-voids of varying sizes exist in most metals and alloys. Both experiments and numerical studies have demonstrated the critical influence of initial void sizes on void growth. The classical Gurson–Tvergaard–Needleman model summarizes the influence of voids with a single parameter, namely the void-volume fraction, excluding any possible effects of the void-size distribution. We extend our newly proposed model including the multi-sized void (MSV) effect and the void-interaction effect for the capability of working for both moderate and high loading rate cases, where either rate dependence or microinertia becomes considerable or even dominant. Parametric studies show that the MSV-related competitive mechanism among void growth leads to the dependence of the void growth rate on void size, which directly influences the voids contribution to the total energy composition. We finally show that the stress–strain constitutive behavior is also affected by this MSV-related competitive mechanism. The stabilizing effect due to rate sensitivity and microinertia is emphasized.

A strain gradient plasticity theory with application to wire torsion

Based on the framework of the existing strain gradient plasticity theories, we have examined three kinds of relations for the plastic strain dependence of the material intrinsic length scale, and thus developed updated strain gradient plasticity versions with deformation-dependent characteristic length scales. Wire torsion test is taken as an example to assess existing and newly built constitutive equations. For torsion tests, with increasing plastic strain, a constant intrinsic length predicts too high a torque, while a decreasing intrinsic length scale can produce better predictions instead of the increasing one, different from some published observations. If the Taylor dislocation rule is written in the Nix-Gao form, the derived constitutive equations become singular when the hardening exponent gets close to zero, which seems questionable and calls for further experimental clarifications on the exact coupling of hardening due to statistically stored dislocations and geometrically necessary dislocations. Particularly, when comparing the present model with the mechanism-based strain gradient plasticity, the present model satisfies the reciprocity relation naturally and gives different predictions even under the same parameter setting.

Taylor-plasticity-based analysis of length scale effects in void growth

We have studied the void growth problem by employing the Taylor-based strain gradient plasticity theories, from which we have chosen the following three, namely, the mechanism-based strain gradient (MSG) plasticity (Gao et al 1999 J. Mech. Phys. Solids 47 1239, Huang et al 2000 J. Mech. Phys. Solids 48 99–128), the Taylor-based nonlocal theory (TNT; 2001 Gao and Huang 2001 Int. J. Solids Struct. 38 2615) and the conventional theory of MSG (CMSG; Huang et al 2004 Int. J. Plast. 20 753). We have addressed the following three issues which occur when plastic deformation at the void surface is unconstrained. (1) Effects of elastic deformation. Elasticity is essential for cavitation instability. It is therefore important to guarantee that the gradient term entering the Taylor model is the effective plastic strain gradient instead of the total strain gradient. We propose a simple elastic–plastic decomposition method. When the void size approaches the minimum allowable initial void size related to the maximum allowable geometrically necessary dislocation density, overestimation of the flow stress due to the negligence of the elastic strain gradient is on the order of near the void surface, where l, eY and R0 are, respectively, the intrinsic material length scale, the yield strain and the initial void radius. (2) MSG intrinsic inconsistency, which was initially mentioned in Gao et al (1999 J. Mech. Phys. Solids 47 1239) but has not been the topic of follow-up studies. We realize that MSG higher-order stress arises due to the linear-strain-field approximation within the mesoscale cell with a nonzero size, le. Simple analysis shows that within an MSG mesoscale cell near the void surface, the difference between microscale and mesoscale strains is on the order of , indicating that when , the higher-order stress effect can make the MSG result considerably different from the TNT or CMSG results. (3) Critical condition for cavitation instability. When Taylor plasticity replaces classical plasticity as the flow rule, the critical cavitation condition, appearing when the derivative of the externally imposed mean stress with respect to the current void radius becomes zero, is rewritten analytically according to the Leibniz relation and found to be very different from the classical counterpart.

Gradient-type modeling of the effects of plastic recovery and surface passivation in thin films

The elasto-plastic responses of thin films subjected to cyclic tension-compression loading and bending are studied, with a focus on Bauschinger and size effects. For this purpose, a model is established by incorporating plastic recovery into the strain gradient plasticity theory we proposed recently. Elastic and plastic parts of strain and strain gradient, which are determined by the elasto-plastic decomposition according to the associative rule, are assumed to have a degree of material-dependent reversibility. Based on the above assumption, a dislocation reversibility-dependent rule is built to describe evolutions of different deformation components under cyclic loadings. Furthermore, a simple strategy is provided to implement the passivated boundary effects by introducing a gradual change to relevant material parameters in the yield function. Based on this theory, both bulge and bending tests under cyclic loading conditions are investigated. By comparing the present predictions with the existing experimental data, it is found that the yield function is able to exhibit the size effect, the Bauschinger effect, the influence of surface passivation and the hysteresis-loop phenomenon. Thus, the proposed model is deemed helpful in studying plastic deformations of micron-scale films.