Thomas E. Wilt

A general hereditary multimechanism-based deformation model with application to the viscoelastoplastic response of titanium alloys

Abstract The formulation of a general model for the hereditary behavior of materials, in the viscoelastic and viscoplastic regimes, is presented. In this, we utilize the complete-potential structure as a general framework, together with the notion of strain- and stress- partitioning in terms of separate contributions of several submechanisms (viscoelastic and viscoplastic) to the thermodynamic functions (stored energy and dissipation). Detailed numerical treatments are given for both (i) the implicit integration algorithm for the governing flow and evolutionary rate equations of the model, and (ii) the automated parameter-estimation methodology (using the software code COMPARE) for characterization. For illustration, a specific form of the model presented is characterized for the TIMETAL 21S material using a very comprehensive test matrix, including creep, relaxation, constant strain-rate tension tests, etc. Discussion of these correlations tests, together with comparisons to several other experimental results, are given to assess the performance and predictive capabilities of the present model as well as the effectiveness and practical utility of the algorithms proposed.

Influence of fiber architecture on the inelastic response of metal matrix composites

Abstract This three-part paper focuses on the effect of fiber architecture (i.e. shape and distribution) on the elastic and inelastic response of unidirectionally reinforced metal matrix composites (MMCs). The first part provides an annotated survey of the literature; it is presented as an historical perspective dealing with the effects of fiber shape and distribution on the response of advanced polymeric matrix composites and MMCs. A summary of the state of teh art will assist in defining new directions in this quickly reviving area of research. The second part outlines a recently developed analytical micromechanics model that is particularly well suited for studying the influence of these effects on the response of MMCs. This micromechanics model, referred to as the generalized method of cells (GMC), can predict the overall inelastic behavior of unidirectional, multiphase composites, given the properties of the constituents. The model is also general enough to predict the response of unidirectional composites that are reinforced by either continuous or discontinuous fibers, with different inclusion shapes and spatial arrangements, in the presence of either perfect or imperfect interfaces and/or interfacial layers. Recent developments on this promising model, as well as directions for future enhancements of the models predictive capability, are included. Finally, the third part provides qualitative results generated by using GMC for a representative titanium matrix composite system, SCS-6/TIMETAL 21S. The results presented correctly demonstrate the relative effects of fiber arrangement and shape on the longitudinal and transverse stress-strain and creep behavior of MMCs, with both strong and weak fiber/matrix interfacial bonds. Fiber arrangements included square, square-diagonal, hexagonal and rectangular periodic arrays, as well as a random array. The fiber shapes were circular, square, and cross-shaped cross-sections. The effect of fiber volume fraction on the stress-strain response is also discussed, as is the thus-far poorly documented strain rate sensitivity effect. In addition to the well-documented features of the architecture-dependent behavior of continuously reinforced two-phase MMCs, new results are presented about continuous multiphase internal architectures. Specifically, the stress-strain and creep responses of composites with different size fibers and different internal arrangements and bond strengths are investigated; the aim was to determine the feasibility of using this approach to enhance the transverse toughness and creep resistance of titanium matrix composites (TMCs).

A mixed element for laminated plates and shells

Formulation and numerical evaluation of a simple shear-flexible four-noded quadrilateral laminated composite plate/shell finite-element is presented. The element developed is based on a generalized mixed variational principle with independently assumed displacement and laminate internal strain fields. For the latter, a layer-number-independent polynomial interpolation is utilized, together with a judicious selection of the in-plane (spanwise) distributions for the strain components. This was facilitated by the use of a set of bubble functions as additional kinematic degrees of freedom, which was shown to be crucial for eliminating the locking phenomenon. For dynamic applications, a simplified lumped mass matrix is employed. Finally, an extensive number of critical test cases are given to access the elements preformance and to illustrate its effectiveness in static as well as vibration problems for anisotropic laminated plates and shells.

A Modeling Investigation of Thermal and Strain Induced Recovery and Nonlinear Hardening in Potential Based Viscoplasticity

Specific forms for both the Gibb’s and the complementary dissipation potentials were chosen such that a complete potential based multiaxial, isothermal, viscoplastic model was obtained. This model, in general, possesses three internal state variables (two scalars associated with dislocation density and one tensor associated with dislocation motion) both thermal and dynamic recovery mechanisms, and nonlinear kinematic hardening. This general model, although possessing associated flow and evolutionary laws, is shown to emulate three distinct classes of theories found in the literature, by modification of the driving threshold function F. A parametric study was performed on a specialized nondimensional multiaxial form containing only a single tensorial internal state variable (i.e., internal stress). The study was conducted with the idea of examining the impact of including a strain-induced recovery mechanism and the compliance operator, derived from the Gibb’s potential, on the uniaxial and multiaxial response. One important finding was that inclusion of strain-induced recovery provided the needed flexibility in modeling stress-strain and creep response of metals at low homologous temperatures, without adversely affecting the high temperature response. Furthermore, for nonproportional loading paths, the inclusion of the compliance operator had a significant influence on the multiaxial response, but had no influence on either uniaxial or proportional load histories.

An anisotropic viscoelastoplastic model for composites—sensitivity analysis and parameter estimation

Abstract Because of their potential in achieving many performance enhancements, composite material systems (e.g. fiber-reinforced composites) are presently called upon to operate under wide range of stresses, temperatures, and loading rates. This in turn requires the development of general material models to capture the significant effects of anisotropy on both elastic and inelastic responses. The starting point in the present contribution is the development of a class of such viscoplastic models. Furthermore, a number of robust, computationally efficient, algorithms are also presented for the development of an overall strategy to estimate the material parameters characterizing these complex models; i.e. rate-dependent plastic flow, non-linear kinematic hardening, thermal/static recovery, anisotropic viscoelastic and viscoplastic flow. The entire procedure is automated through an integrated software namely, COnstitutive Material PARameter Estimator, COMPARE, to enable the determination of an ‘optimum’ set of material parameters by minimizing the errors between the experimental test data and the predicted response. The key ingredients of COMPARE are (i) primal analysis, (ii) sensitivity analysis, (iii) a gradient-based optimization problem and a (iv) graphical user interface. The estimation of the material parameters is cast as a minimum-error, weighted multi-objective, non-linear optimization problem with constraints. Detailed derivations of the direct differentiation sensitivity expressions are presented. In addition, numerical comparisons of the sensitivities obtained by the more traditional finite difference approaches are given to assess accuracy. Results generated by applying the developed algorithms for anisotropic, strain-controlled tensile (with comparison to typical experimental data) and constant-stress creep tests are presented to demonstrate the ability of the present models to accurately capture time-dependent anisotropic material behavior.

Fracture toughness computational simulation of general delaminations in fiber composites

A procedure is described to computationally simulate composite laminate fracture toughness in terms of strain energy release rate (SERR). It is also used to evaluate the degradation in laminate structural integrity in terms of displacements, loss in stiffness, loss in vibration frequencies and loss in buckling resistance. Specific laminates are selected for detail studies in order to demonstrate the generality of the procedure. These laminates had center delaminations, off-center delaminations, and pocket delaminations (center and off-center) at the free-edge and center delaminations at the interior. The lami nates had two different thicknesses and were made from three different materials. The results obtained are presented in graphical form to illustrate the effects of delamination on the laminate structural integrity and on the laminate strain energy release rate (composite fracture toughness).

A coupled/uncoupled computational scheme for deformation and fatigue damage analysis of unidirectional metal-matrix composites

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum-based fatigue damage model for unidirectional metal-matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress that fully couples the fatigue damage calculations with the finite element deformation solution. Two applications using the fatigue damage algorithm are presented. First, an axisymmetric stress analysis of a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. Second, a micromechanics analysis of a fiber/ matrix unit cell using both the finite element method and the generalized method of cells (GMC). Results are presented in the form of S-N curves and damage distribution plots.