Effective Plastic Strain Curves Research Articles

Material parameters for pressure-dependent yielding of unidirectional fiber-reinforced polymeric composites

We study elasto-plastic deformations of unidirectional fiber reinforced polymeric composites (UFPCs) with fibers assumed to deform elastically and the matrix elasto-plastically. The matrix’s and hence composite’s plastic deformations are analyzed by using both the pressure-independent von Mises yield surface and the pressure-dependent Drucker–Prager yield surface and the associated flow rules. In both cases the strain hardening of the matrix is considered and values of material parameters for the matrix are obtained by computing the effective stress versus the effective plastic strain curves from experimental uniaxial stress–strain curves. Values of parameters in the yield surface for the UFPC in terms of those of the matrix and the volume fraction of fibers are found by using a micromechanics approach. Wherever possible, the computed results are compared with the corresponding experimental findings available in the literature. Significant contributions of the work include providing a methodology for determining values of elasto-plastic material parameters for a UFPC from those of its constituents and their volume fractions, and giving expressions in terms of volume fractions of fibers for material parameters appearing in the yield surface of the composite.

Elastic–plastic-hydrodynamic analysis of crater blasting in steel fiber reinforced concrete

This paper presents a numerical analysis of crater blasting in steel fiber reinforced concrete (SFRC). In order to model the nonlinear damage-softening behavior of SFRC, the effective stress and effective plastic strain curve is tabulated and used as input for the material Type10 (MAT_ELASTIC_PLASTIC_HYDRO) available in LS-DYNA. The Gruneisen equation of state (EOS) is used to model the pressure volume relationship. With the two erosion criteria namely tensile cut-off and failure strain incorporated, the crater blasting in SFRC is simulated. Numerical results show that the adopted model and high-pressure EOS can well capture the main characteristics and failure process of SFRC under blast loading, and the related parameters can be determined conveniently. In addition, the volume fraction of fibers exerts a significant influence on the dimension of blast-induced crater.

A 3-D Finite Deformation Anisotropic Visco-Plasticity Model for Fiber Composites

A 3-D finite deformation anisotropic visco-plasticity model is presented for fiber composites in total Lagrangian co-ordinates. The plastic potential function is given by a quadratic function in stresses in the local co-ordinates system of the lamina. The model is used to derive the anisotropic plastic constitutive relation of a woven composite made of S-2 glass fibers embedded in polyester resinwith approximately 60% by weight of fibers. The coefficients of the constitutive model are experimentally determined through off-axis tension tests and out-of-plane shear tests. Off-axis tension tests are carried out by varying the angle between the fiber orientation and loading direction. The measured stress-strain curves are used to derive a master effective stress–effective plastic strain curve, which is described by two power laws. Amodified Arcan fixture is used to carry out pure shear tests to determine the out-of-plane shear coefficient. Compression tests are carried out to establish the material compressive response in the plane of the lamina and along the fiber direction. The anisotropic plasticity model is integrated into the in-house finite element code FEAP98. Numerical analyses are carried out for the off-axis tension tests and compression tests. These analyses show that the model reasonably predicts the constitutive response of wovenGRPcomposites in confirmation with the experimental data. The model further incorporates strain rate and temperature dependence on the anisotropic plastic flow constitutive law. Ballistic penetration simulations are carried out using the integrated code. The velocity at the back surface of the composite target, obtained by analyses, is compared with the data measured experimentally using interferometry. Insight into the failure process is obtained through analysis of different energy dissipation mechanisms.

Failure mode transition speeds in an impact loaded prenotched plate with four thermoviscoplastic relations

Four different thermoviscoplastic relations, namely, the Litonski–Batra, Johnson–Cook, Bodner–Partom and the power law are used to model the thermoviscoplastic response of a material. Each one of these relations accounts for strain hardening, strain-rate hardening and thermal softening of the material. The material parameters in these relations are found by solving an initial-boundary-value problem corresponding to simple shearing deformations so that the computed effective stress vs. the effective plastic strain curves match closely with the experimental data of Marchand and Duffy who tested thin-walled HY-100 steel tubes in torsion. These four viscoplastic relations are used to analyze dynamic thermomechanical deformations of a prenotched plate impacted on the notched side by a cylindrical projectile made of the same material as the plate. The impact loading on the contact surface is simulated by prescribing the time history of the normal component of velocity and null tangential tractions. A plane strain state of deformation is assumed to prevail in the plate and its deformations are studied for different values of the impact speed. The in-house developed finite element code employs constant strain triangular elements, one point integration rule, and a lumped mass matrix. The Lagrangian description of motion is used to describe deformations of the plate. The coupled nonlinear partial differential equations are first reduced to coupled nonlinear ordinary differential equations (ODEs) by using the Galerkin approximation. The ODEs are integrated by using the stiff solver, LSODE, which adaptively adjusts the time step size and computes the solution within the prescribed accuracy. Results computed with the four constitutive relations are found to be qualitatively similar to each other and the general trends agree with the experimental observations in the sense that at low speed of impact, a brittle failure ensues at a point on the upper surface of the notch tip. However, at high impact speeds, a ductile failure in the form of a shear band initiates first from a point on the lower surface of the notch tip. The predicted speed at which the failure mode transitions from brittle to ductile is different for the four viscoplastic relations. The effects of the notch tip radius and the yield strength of the material in a quasistatic simple tension/compression test on the failure-mode transition speed have been ascertained.

Anisotropic yield functions with plastic-strain-induced anisotropy

Abstract In most anisotropic yield functions, the stress exponent, M , associated with the shape of the yield surface is usually independent of plastic-strain accumulation. This does not allow for different work-hardening characteristics under various strain states, as has been observed in aluminum alloys. Assuming coefficients characterizing anisotropy do not change with plastic deformation, the M value should vary with plastic strain, relaxing the isotropic hardening assumption. To verify this, plane-strain tests along with numerical analysis were carried out with 2008-T4 aluminium and 70/30 brass. The effective stress and effective plastic-strain curve assuming plane strain and plane stress was fit to the corresponding stress-strain data obtained in uniaxial tension. This was done by allowing M value to vary with effective plastic-strain. Hill's 1979 (case iv),Hosford's 1979 and Barlat's 1991 (6 component) yield functions were evaluated. Results showed that, with all the yield functions tested, the aluminum exhibited substantial variation of M value especially at larger strains while the brass showed minor change. Relevant numerical analysis indicated that, even though all the yield functions showed noticeable changes of M as strain increases in order for the plane-strain curve to match with the uniaxial curve, this variation of M will not affect much to the prediction with Hosford's and Barlat's yield functions, of which the typically valid M is much higher than that of Hill's. FEM simulation of plane-strain sheet forming with 2008-T4 aluminium alloy verified that implementation of varying M -value with Hill's yield function led to better agreement with experimental measurements, while the variation of M with Barlat's yield function exhibited little influence on the strain prediction.