Stress analysis of thin elasto-plastic shells
Stress analysis of thin elastoplastic shells with large displacements loaded into strain hardening range, assuming plastic strain incompressibility
Hyman, B.↗
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Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method
A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.
Rzasnicki, W.↗
Finite element analysis of elasto-plastic soils. Report no. 4: Finite element analysis of elasto-plastic frictional materials for application to lunar earth sciences
The behavior of finite element models employing different constitutive relations to describe the stress-strain behavior of soils is investigated. Three models, which assume small strain theory is applicable, include a nondilatant, a dilatant and a strain hardening constitutive relation. Two models are formulated using large strain theory and include a hyperbolic and a Tresca elastic perfectly plastic constitutive relation. These finite element models are used to analyze retaining walls and footings. Methods of improving the finite element solutions are investigated. For nonlinear problems better solutions can be obtained by using smaller load increment sizes and more iterations per load increment than by increasing the number of elements. Suitable methods of treating tension stresses and stresses which exceed the yield criteria are discussed.
Marr, W. A., Jr.↗
The relation between the tensile strength and the hardness of metals
This report presents methods determining the hardness and tensile strength of metals by showing the effect and dependence of the hardness numbers on the strain-hardening. Relations between the hardness numbers and the ordinary stress-strain diagrams and tensile strength are given. Procedures for finding the Brinell strength are also presented.
METALS - NICKEL HARDNESS TESTS↗
Influence of cobalt, tantaum and tungsten on the high temperature mechanical properties of single crystal nickel-base superalloys
For alloys with the baseline refractory metal level of 3 percent Ta and 10 percent W, decreases in Co level from 10 to 0 percent resulted in increased tensile strength and creep resistance. Substitution of W for Ta resulted in decreased creep life at high stresses but improved life at low stresses. Substitution of Ni for Ta caused large reductions in tensile strength and creep resistance, and corresponding increases in ductility. For these alloys with low Ta plus W totals, strength was independent of Co level. The increases in tensile strength with increases in refractory metal content were related to the increases in gamma volume fraction and solid solution hardening. Increases in strength as Co level decreased were considered to be the result of coherency strain hardening from the increased lattice mismatch. Dislocation shear through the gamma-gamma interface is considered to be the rate limiting step in the deformation process.
Nathal, M. V.↗
Application of an Uncoupled Elastic-plastic-creep Constitutive Model to Metals at High Temperature
A uniaxial, uncoupled constitutive model to predict the response of thermal and rate dependent elastic-plastic material behavior is presented. The model is based on an incremental classicial plasticity theory extended to account for thermal, creep, and transient temperature conditions. Revisions to he combined hardening rule of the theory allow for better representation of cyclic phenomenon including the high rate of strain hardening upon cyclic reyield and cyclic saturation. An alternative approach is taken to model the rate dependent inelastic deformation which utilizes hysteresis loops and stress relaxation test data at various temperatures. The model is evaluated and compared to experiments which involve various thermal and mechanical load histories on 5086 aluminum alloy, 304 stainless steel and Hastelloy-X.
Haisler, W. E.↗
Finite-strain large-deflection elastic-viscoplastic finite-element transient response analysis of structures
A method of analysis for thin structures that incorporates finite strain, elastic-plastic, strain hardening, time dependent material behavior implemented with respect to a fixed configuration and is consistently valid for finite strains and finite rotations is developed. The theory is formulated systematically in a body fixed system of convected coordinates with materially embedded vectors that deform in common with continuum. Tensors are considered as linear vector functions and use is made of the dyadic representation. The kinematics of a deformable continuum is treated in detail, carefully defining precisely all quantities necessary for the analysis. The finite strain theory developed gives much better predictions and agreement with experiment than does the traditional small strain theory, and at practically no additional cost. This represents a very significant advance in the capability for the reliable prediction of nonlinear transient structural responses, including the reliable prediction of strains large enough to produce ductile metal rupture.
Rodal, J. J. A.↗
Fatigue crack tip deformation and fatigue crack propagation
The effects of stress ratio, prestress cycling and plate thickness on the fatigue crack propagation rate are studied on 2024-T351 aluminum alloy. Fatigue crack propagation rate increases with the plate thickness and the stress ratio. Prestress cycling below the static yield strength has no noticeable effect on the fatigue crack propagation rate. However, prestress cycling above the static yield strength causes the material to strain harden and increases the fatigue crack propagation rate. Crack tip deformation is used to study the fatigue crack propagation. The crack tip strains and the crack opening displacements were measured from moire fringe patterns. The moire fringe patterns were obtained by a double exposure technique, using a very high density master grille (13,400 lines per inch).
Kang, T. S.↗
High temperature low-cycle fatigue mechanisms in single crystals of nickel-based superalloy Mar-M 200
Twenty three high temperature low-cycle fatigue tests were conducted on single crystals of the nickel-based superalloy Mar-M 200. Tests were conducted at 760 and 870 C. SEM fractography and transmission electron microscopy were used to determine mechanisms responsible for the observed orientation dependent fatigue behavior. It has been concluded that the plastic characteristics of the alloy lead to orientation-dependent strain hardening and fatigue lives at 760 C. At 870 C, the elastic characteristics of the alloy dominated the behavior, even though the plastic strain ranges were about the same as they were at 760 C. This led to orientation-dependent fatigue lives, but the trends were not the same as they were at 760 C.
Milligan, W. W.↗
Multiscale Modeling of Structurally-Graded Materials Using Discrete Dislocation Plasticity Models and Continuum Crystal Plasticity Models
A multiscale modeling methodology that combines the predictive capability of discrete dislocation plasticity and the computational efficiency of continuum crystal plasticity is developed. Single crystal configurations of different grain sizes modeled with periodic boundary conditions are analyzed using discrete dislocation plasticity (DD) to obtain grain size-dependent stress-strain predictions. These relationships are mapped into crystal plasticity parameters to develop a multiscale DD/CP model for continuum level simulations. A polycrystal model of a structurally-graded microstructure is developed, analyzed and used as a benchmark for comparison between the multiscale DD/CP model and the DD predictions. The multiscale DD/CP model follows the DD predictions closely up to an initial peak stress and then follows a strain hardening path that is parallel but somewhat offset from the DD predictions. The difference is believed to be from a combination of the strain rate in the DD simulation and the inability of the DD/CP model to represent non-monotonic material response.
Saether, Erik↗
Development and Characterization of a Rate-Dependent Three-Dimensional Macroscopic Plasticity Model Suitable for Use in Composite Impact Problems
Several key capabilities have been identified by the aerospace community as lacking in the material/models for composite materials currently available within commercial transient dynamic finite element codes such as LS-DYNA. Some of the specific desired features that have been identified include the incorporation of both plasticity and damage within the material model, the capability of using the material model to analyze the response of both three-dimensional solid elements and two dimensional shell elements, and the ability to simulate the response of composites composed with a variety of composite architectures, including laminates, weaves and braids. In addition, a need has been expressed to have a material model that utilizes tabulated experimentally based input to define the evolution of plasticity and damage as opposed to utilizing discrete input parameters (such as modulus and strength) and analytical functions based on curve fitting. To begin to address these needs, an orthotropic macroscopic plasticity based model suitable for implementation within LS-DYNA has been developed. Specifically, the Tsai-Wu composite failure model has been generalized and extended to a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The coefficients in the yield function are determined based on tabulated stress-strain curves in the various normal and shear directions, along with selected off-axis curves. Incorporating rate dependence into the yield function is achieved by using a series of tabluated input curves, each at a different constant strain rate. The non-associative flow-rule is used to compute the evolution of the effective plastic strain. Systematic procedures have been developed to determine the values of the various coefficients in the yield function and the flow rule based on the tabulated input data. An algorithm based on the radial return method has been developed to facilitate the numerical implementation of the material model. The presented paper will present in detail the development of the orthotropic plasticity model and the procedures used to obtain the required material parameters. Methods in which a combination of actual testing and selective numerical testing can be combined to yield the appropriate input data for the model will be described. A specific laminated polymer matrix composite will be examined to demonstrate the application of the model.
Impact↗
Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems
The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.
Impact↗
Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems
The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.
Impact↗
Effect of misalignment on mechanical behavior of metals in creep
Application of the endochronic theory of viscoplasticity to creep, creep recovery, and stress relaxation at the small strain and short time range produced the following results: (1) The governing constitutive equations for constant-strain-rate stress-strain behavior, creep, creep recovery, and stress relaxation were derived by imposing appropriate constraints on the general constitutive equation of the endochronic theory. (2) A set of material constants was found which correlate strain-hardening, creep, creep recovery, and stress relaxation. (3) The theory predicts with reasonable accuracy the creep and creep recovery behaviors at short time. (4) The initial strain history prior to the creep stage affects the subsequent creep significantly. (5) A critical stress was established for creep recovery. A computer program, written for the misalignment problem is reported.
Wu, H. C.↗
Tensile deformation of 2618 and Al-Fe-Si-V aluminum alloys at elevated temperatures
The present study experimentally characterizes the effects of elevated temperature on the uniaxial tensile behavior of ingot metallurgy 2618 Al alloy and the rapidly solidified FVS 0812 P/M alloy by means of two constitutive formulations: the Ramberg/Osgood equation and the Bodner-Partom (1975) incremental formulation for uniaxial tensile loading. The elastoplastic strain-hardening behavior of the ingot metallurgy alloy is equally well represented by either formulation. Both alloys deform similarly under decreasing load after only 1-5 percent uniform tensile strain, a response which is not described by either constitutive relation.
Leng, Y.↗
Endochronic theory of transient creep and creep recovery
Short time creep and creep recovery were investigated by means of the endochronic theory of viscoplasticity. It is shown that the constitutive equations for constant-strain-rate stress-strain behavior, creep, creep recovery, and stress relaxation can all ber derived from the general constitutive equation by imposing appropriate constraints. In this unified approach, the effect of strain-hardening is naturally accounted for when describing creep and creep recovery. The theory predicts with reasonable accuracy the creep and creep recovery behaviors for Aluminum 1100-0 at 150 C. It was found that the strain-rate history at prestraining stage affects the subsequent creep. A critical stress was also established for creep recovery. The theory predicts a forward creep for creep recovery stress greater than the critical stress. For creep recovery stress less than the critical stress, the theory then predicts a normal strain recovery.
Wu, H. C.↗
Sensitivity of inelastic response to numerical integration of strain energy
The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.
Kamat, M. P.↗
Tensile and compressive behavior of Borsic/aluminum
The results of an experimental investigation of the mechanical behavior of Borsic/aluminum are presented. Composite laminates were tested in tension and compression for monotonically increasing load and also for variable loading cycles in which the maximum load was increased in each successive cycle. It is shown that significant strain-hardening, and corresponding increase in yield stress, is exhibited by the metal matrix laminates. For matrix dominated laminates, the current yield stress is essentially identical to the previous maximum stress, and unloading is essentially linear with large permanent strains after unloading. For laminates with fiber dominated behavior, the yield stress increases with increase in the previous maximum stress, but the increase in yield stress does not keep pace with the previous maximum stress. These fiber dominated laminates exhibit smaller nonlinear strains, reversed nonlinear behavior during unloading, and smaller permanent strains after unloading. Compression results from sandwich beams and flat coupons are shown to differ considerably. Results from beam specimens tend to exhibit higher values for modulus, yield stress, and strength.
Herakovich, C. T.↗