Showing papers on "Viscoplasticity published in 1991"

Mechanics of Composite Materials: A Unified Micromechanical Approach

Abstract: 1. Fundamentals of the Mechanics of Composites. Representative volume element. Volumetric averaging. Homogeneous boundary conditions. Average strain theorem. Average stress theorem. Effective elastic moduli. Relations between averages-direct approach. Relations between averages - energy approach. 2. Basic Models in the Mechanics of Composites. The Voigt approximation. The Reuss approximation. Hill's theorem. The dilute approximation. The composite spheres model. The self-consistent scheme. The generalized self-consistent scheme. The differential scheme. The mori-tanaka theory. Exhelby equivalent inclusion method. 3. The Micromechanical Method of Cells. The method of cells for fiber reinforced materials. Coefficients of thermal expansion. Hill's relations. Thermal conductivities. Specific heats. The method of cells for short-fiber composites. Randomly reinforced materials. Periodically billlminated materials. 4. Strength and Fatigue Failure. Micromechanics prediction of composite failure. 5. Viscoelastic Behaviour of Composites. Linearly viscoelastic composites. Thermoviscoelastic behaviour of composites. Nonlinear viscoelastic behaviour of composites. 6. Nonlinear Behaviour of Resin Matrix Composites. Macromechanical analysis. Micromechanical analysis. 7. Initial Yield Surfaces of Metal Matrix Composites. The initiation of yielding in isotropic materials. Initial yielding of metal matrix composites. Investigation of the convexity of initial yield surfaces. 8. Inelastic Behaviour of Metal Matrix Composites. Constitutive equations of plasticity. Unified theories of viscoplasticity. Bodner-partom viscoplastic equations. Inelastic behaviour of laminated media. Inelastic behaviour of fibrous composites. Matrix mean-field and local-field. Subsequent yield surfaces prediction of metal matrix composites. Metal matrix composite laminates. Short-fiber metal-matrix composites. 9. Imperfect Bonding in Composites. General considerations. The flexible interface imperfect bonding model. Periodically billaminated materials. Fiber-reinforced materials. Short-fiber and particulate composites. The Coulomb frictional law for the modeling of interfacial damage in composites. Index.

Solid and fluid mechanics dynamics and non-linearity

Abstract: Plate and Shell bending approximation - thin (Kirchhoff) plates and C1 continuity requirements "Thick" Reissner-Mindlin plates - irreducible and mixed formulations shells as an assembly of flat elements axisymmetric shells shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions semi-analytical finite element processes - use of orthogonal functions and "Finite Strip" methods non-linear problems - plasticity, creep (viscoplasticity), non-linear field problems, etc. geometrically non-linear problems - large displacement and structural instability the time dimension - semi-discretization of field and dynamic problems and analytical solution procedures the time dimension - discrete approximation in time coupled systems convection dominated problems fluid mechanics - governing equations an incompressible flow Newtonian and non-Newtonian viscous flows compressible high-speed gas flow shallow water equations and waves computer procedures for finite element anlaysis.

A User-Material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program

Abstract: A user-material subroutine has been written to incorporate single crystal plasticity in the fmite element program ABAQUS. The fmite-element formulation of elastic-plastic and viscoplastic single crystal deformation is reviewed in this paper. including versions for small deformation theory and for the rigorous theory of finite-strain and fmite-rotation. Inelastic deformation of a single crystal arises from crystalline slip, which is assumed here to obey the Schmid law. Various self and latent hardening relations between resolved shear stress and shear strain in slip systems are presented and incorporated as options in the subroutine.

An arbitrary Lagrangian-Eulerian finite element method for large deformation analysis of elastic-viscoplastic solids

Abstract: Analysis of large deformation of elastic-viscoplastic materials has been performed in this paper using the finite element method with the arbitrary Lagrangian-Eulerian description. An overstress type viscoplastic model using the internal variable approach in a rotated stress-strain space characterizes the material. Stable and efficient integration techniques for the viscoplastic relations are discussed. A linearized form in the ALE description is presented which is to be solved using iteration techniques. In particular the quasi-Newton methods have been used in this analysis. Several test problems which have been considered illustrate the effectiveness of the entire solution algorithm.

Dynamic Strain Localization in Fluid‐Saturated Porous Media

Abstract: The fluid‐saturated medium is viewed as a two‐phase continuum consisting of a solid porous skeleton with interconnected voids that are filled with a perfect fluid, and the formulation based on the theory of mixtures. Conditions for dynamic strain localization to occur in the rate‐independent elastic‐plastic saturated porous solid are first discussed. In particular, it is shown that the existence of a stationary discontinuity is only dependent upon the material properties of the underlying drained porous solid skeleton. Viscoplasticity is then introduced as a general procedure to regularize the elastic‐plastic porous solid, especially for those situations in which the underlying inviscid drained material exhibits instabilities that preclude meaningful analysis of the initial‐value problem. Rate‐dependency naturally introduces a length scale that sets the width of the shear bands in which the deformations localize and high strain gradients prevail. Then, provided that the element size is appropriate for an ...

Non‐linear B‐stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity

Abstract: A class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward-Euler return maps as a particular case. More importantly, it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary Helmholz free energy function (B-stability). Since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm, the requirement of B-stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity. The analysis that follows depends critically on the assumption of convexity. In particular, the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation. The proposed algorithms obey the discrete counterpart of this classical principle.

Elastic/Viscoplastic Constitutive Model for Fiber Reinforced Thermoplastic Composites

Abstract: A constitutive model to describe the elastic/viscoplastic behavior of fiber-reinforced thermoplastic composites under plane stress conditions is presented. Formulations are given for quasi-static plasticity and time-dependent viscoplasticity. Experimental procedures required to generate the necessary material constants are explained, and the experimental data is compared to the predicted behavior.

Characterization of Elastic-Viscoplastic Properties of an AS4/PEEK Thermoplastic Composite:

Abstract: The elastic-viscoplastic properties of an AS4/PEEK (APC-2) thermoplastic composite were characterized at 24 C (75 F) and 121 C (250 F) by using a one-parameter viscoplasticity model. To determine the strain-rate effects, uniaxial tension tests were performed on unidirectional off-axis coupon specimens with different monotonic strain rates. A modified Bodner and Partom's model was also used to describe the viscoplasticity of the thermoplastic composite. The experimental results showed that viscoplastic behavior can be characterized quite well using the one-parameter overstress viscoplasticity model.

Nonlinear stability of the time-discrete variational problem of evolution in nonlinear heat conduction, plasticity and viscoplasticity

Abstract: A rigorous nonlinear stability analysis for a claa of return mapping algorithms in plasticity and viscoplasticity based on the generalized mid-point rule is presented. In contrast with previous developments, the analysis is performed directly on the system of variational inequalities governing the problem and shown to hold for non-smooth convex elastic domains. To motivata the approach, a similar analysis is performed on the nonlinear heat-conduction equation.

A viscoplastic theory with thermodynamic considerations

Abstract: A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity for initially isotropic materials. Three, fundamental, internal, state variables are admitted; they are: a tensorial back stress for kinematic effects, and scalar drag and yield strengths for isotropic effects. All three are considered to evolve phenomenologically according to competitive processes between strain hardening, deformation induced dynamic recovery, and thermally induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is proposed. The theory allows each of the three internal variables to be composed as a sum of independently evolving constituents. The evolution of internal state can also include terms that vary linearly with the external variable rates, whose presence affects the energy dissipation properties of a material.

The influence of microstructure-induced gradients on the localization of deformation in viscoplastic materials

Abstract: We suggest here a generalization of the conventional constitutive models of viscoplasticity. This is accomplished by the inclusion of spatial gradients of the equivalent stress and strain in the evolution equation for the equivalent plastic strain rate. We restrict attention to plane deformation and elastic effects are neglected for simplicity. The implications of the new terms in the constitutive model are discussed for the case of a general eigenvalue problem of an initially homogeneous and stationary viscous flow. It turns out that the nonclassical material parameters can be chosen in such a way that the governing differential equations are always strongly elliptic irrespective of whether the mateiral is strain softening. As it is well known, the latter typically leads to loss of ellipticity in the conventional theories. Explicit results are presented for the case of a shear band instability. Within the framework of the present theory, and in contrast to conventional models, the shear band kinematics have a well defined geometrical structure.

The strength behavior of granulated silicon carbide at high strain rates and confining pressure

Abstract: The dynamic Mohr–Coulomb behavior of silicon carbide (SiC) was inferred from symmetric pressure/shear plate‐impact experiments which entail planar impact of two SiC plates inclined at 15° to the impact direction. The transverse velocity of the free rear surface of the target plate was recorded using a laser Doppler velocimeter system, and the experiments were simulated using a postulated viscoplastic constitutive model that accounts for comminution and dilatancy. Model parameters were varied until the computed and measured velocity histories agreed. The results indicate that comminution occurred soon after loading, and thus the experiment measures the behavior of granulated material at shear strain rates of ≊105 s−1 and mean stress ranging from 1 to 9 GPa. A friction coefficient of 0.23 was obtained, which is about half the value for quasistatic compression of precomminuted ceramic reported in the literature. The simulation results were strongly affected by the values chosen for the friction coefficient a...

Viscoplastic deformation analysis and extrusion die design by FEM

Abstract: A viscoplastic model for extrusion is discussed which simultaneously predicts the deformation field, optimal die geometry, and plastic boundaries. The die geometry and plastic boundaries are expressed in terms of chosen trial functions that satisfy certain geometrical and physical constraints. The variational power integral is minimized in the trial plastic domain using FEM technique to determine the deformation field and shape coefficients for the die contour and plastic boundaries. The proposed method is implemented for the optimal design of an axisymmetric streamlined die. The predicted values are in reasonable agreement with the experimental observations and are in conformity with the results published earlier.

An adaptive descent method for non‐linear viscoplasticity

Abstract: A forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains. A significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems. The resultant non-linear system of equations is solved by an adaptive descent method which combines the rapid convergence of Newton's method near the solution with the robustness of a method of successive approximations. The use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate-insensitive range of behaviours exhibited, for example, by metals at low temperature, where slow convergence of the non-linear solution algorithm has traditionally hampered their use.

A new uniformly valid asymptotic integration algorithm for elasto‐plastic creep and unified viscoplastic theories including continuum damage

Abstract: A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

Experimental and finite element simulation methods for rate‐dependent metal forming processes

Abstract: An experimental procedure and a finite element simulation method for rate-dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross-section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton-Raphson incremental-iterative method which solves the non-linear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress-strain curves (quasi-static and constant strain rate), which are used to establish a rate-dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.