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Abstract
We consider a problem of modeling fracture and failure preceded by large scale yielding of ductile shells from the point of view of large-scale structural analysis. We place a special emphasis on the computational efficiency of the constitutive formulation. In this context, we seek the formulation embedded in the shell mechanics framework, which is both theoretically sound and easily implementable into a large-scale explicit dynamic finite element code without precluding vectorization or parallelization. This is achieved through the elasto-plastic damage constitutive ...
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Abstract
We present a theoretical model to calculate the flexural rigidity of nanowires from three-dimensional elasticity theory that incorporates the effects of surface stress and surface elasticity. The unique features of the model are that it incorporates, through the second moment, the heterogeneous nature of elasticity across the nanowire cross section, and that it accounts for transverse surface-stress-induced relaxation strains. The model is validated by comparison to benchmark atomistic calculations, existing one-dimensional surface elasticity theories based on the Young–Laplace equation, and also ...
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Abstract
During the past two decades, twinning and slip in hexagonal close-packed structures have been extensively studied using molecular dynamics. However, the simulation methods and corresponding results have rendered different conclusions regarding the active twin modes and their mechanisms for nucleation and growth. The nucleation mechanisms for twinning in hexagonal close-packed polycrystalline materials are known to depend strongly on grain boundary orientations, but little is known of the exact mechanisms that occur. The variability in the experimental behavior of single crystals reported ...
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Abstract
We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg–Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase-fields. The main challenge addressed here is encoding various electromechanical crack ...
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Abstract
A couple stress crystal plasticity formulation that incorporates interfacial couple stress energy was proposed in terms of the virtual work-rate principle for finite element method. By applying the assumed constitutive models of couple stress at the grain boundary as well as the grain interior, finite element simulations were conducted for various crystal models, with different grain subdivision models to examine how plastic deformation work is affected by grain subdivision from the interfacial couple stress energy effect. Finite element simulation results showed ...
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Abstract
A physically motivated theory of rubber reinforcement based on filler cluster mechanics is presented considering the mechanical behaviour of quasi-statically loaded elastomeric materials subjected to arbitrary deformation histories. This represents an extension of a previously introduced model describing filler induced stress softening and hysteresis of highly strained elastomers. These effects are referred to the hydrodynamic reinforcement of rubber elasticity due to strain amplification by stiff filler clusters and cyclic breakdown and re-aggregation (healing) of softer, already damaged filler clusters. The theory ...
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Abstract
The steady-state solution for an elastic half-plane under a moving frictionless smooth indenter of arbitrary shape is derived based on the corresponding transient problem and on a condition concerning energy fluxes. Resulting stresses and displacements are found explicitly starting from their expressions in terms of a single analytical function. This solution incorporates all speed ranges, including the super-Rayleigh subsonic and intersonic speed regimes, which received no final description to date. Next, under a similar formulation the wedging of an elastic plane ...
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Abstract
A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations ...
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Abstract
The characteristics of phonons, i.e. linearized normal modes of vibration, provide important insights into many aspects of crystals, e.g. stability and thermodynamics. In this paper, we use the Objective Structures framework to make concrete analogies between crystalline phonons and normal modes of vibration in non-crystalline but highly symmetric nanostructures. Our strategy is to use an intermediate linear transformation from real-space to an intermediate space in which the Hessian matrix of second derivatives is block-circulant. The block-circulant nature of the Hessian enables ...
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Abstract
The Discrete Element Method (DEM) is increasingly used to simulate the behavior of rock. Despite their intrinsic capability to model fracture initiation and propagation starting from simple interaction laws, classical DEM formulations using spherical discrete elements suffer from an intrinsic limitation to properly simulate brittle rock behavior characterized by high values of UCS/TS ratio associated with non-linear failure envelopes, as observed for hard rock like granite. The present paper shows that the increase of the interaction range between the spherical discrete ...
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Abstract
Using a recent elasto-plastic theory of dislocation and disclination fields, a continuous representation of grain boundaries is introduced. Periodic arrays of wedge disclination dipoles, including those defined in the Disclination Structural Unit Model, are set-up as initial configurations in a dynamic model for symmetric tilt boundaries. These configurations are found to be unstable when the transport of disclinations is allowed. Driven by their self couple-stress field, the motion of disclinations leads to relaxation of the initial elastic curvature and stress fields ...
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Abstract
We utilize classical molecular dynamics to study surface effects on the piezoelectric properties of ZnO nanowires as calculated under uniaxial loading. An important point to our work is that we have utilized two types of surface treatments, those of charge compensation and surface passivation, to eliminate the polarization divergence that otherwise occurs due to the polar (0001) surfaces of ZnO. In doing so, we find that if appropriate surface treatments are utilized, the elastic modulus and the piezoelectric properties for ZnO ...
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Abstract
It is by now well-known that micron-sized metallic crystals exhibit a smaller-being-stronger size effect: the yield strength Ï varies with specimen size D approximately as a power law Ï∼D−m, and the exponent m has been found to vary within a range of ∼0.3 to ∼1.0 for different metals. However, little is known about why such a power law comes into play, and what determines the actual value of the exponent m involved. This work shows that if the yield strength is ...
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Abstract
A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, ...
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Abstract
An analytical model of peeling of an elastic tape from a substrate is presented for large deformations and scenarios where sliding occurs in the adhered regions, with this motion resisted by interfacial shear tractions. Two geometries are considered: the first has a free end of the tape being pulled (single-sided peeling), and the second has a detached segment of the tape forming the shape of an inverted letter ‘V’ (double-sided peeling) between adhered sections. The mechanics of peeling is analyzed in ...
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Abstract
This paper presents a new method for ascertaining residual stress fields in engineering components. Diffraction data are employed with a finite element discretization to determine the macroscopic (continuum) residual stress field over the workpiece simultaneously with the crystal-scale distribution of elastic strains at each diffraction measurement point. Stress equilibrium and traction free boundary conditions constrain the solution at the continuum scale. The thousands of lattice strain measurements made at each diffraction volume ensure that the stress solution is consistent with crystal-scale ...
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Abstract
A solution is constructed for the problem of the overall elastic response of ideal (Gaussian or, equivalently, Neo-Hookean) rubber reinforced by a dilute isotropic distribution of rigid particles under arbitrarily large deformations. The derivation makes use of a novel iterative homogenization technique in finite elasticity that allows to construct exact solutions for the homogenization problem of two-phase nonlinear elastic composites with particulate microstructures. The solution is fully explicit for axisymmetric loading, but is otherwise given in terms of an Eikonal partial ...
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Abstract
In Part I, an exact solution was determined for the problem of the overall nonlinear elastic response of Gaussian (or Neo-Hookean) rubber reinforced by a dilute isotropic distribution of rigid particles. Here, this fundamental result is utilized to construct an approximate solution for non-Gaussian rubber reinforced by an isotropic distribution of rigid particles at finite concentration. This is accomplished by means of two different techniques in two successive steps. First, the dilute solution is utilized together with a differential scheme in ...
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Abstract
We present a real-space formulation for coarse-graining Kohn–Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the ...
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Abstract
When guest atoms diffuse into a host solid and react, the host may flow inelastically. Often a reaction can stimulate flow in a host too brittle to flow under a mechanical load alone. We formulate a theory of reactive flow in solids by regarding both flow and reaction as nonequilibrium processes, and placing the driving forces for flow and reaction on equal footing. We construct chemomechanical rate-dependent kinetic models without yield strength. In a host under constant stress and chemical potential, ...
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Abstract
An energy release rate based “fracture” model is presented, which is able to describe unstable dielectric breakdown of ceramic and polymer insulators. The electric field and electrostatic energy of an electrically conducting filament within a spheroidal surface electrode is calculated. As space charge injection is allowed the electric field singularity at the electrical conducting filament is reduced. As a consequence it is possible to solve the electrostatic problem even for filaments where the diameter is reduced to zero and the energy ...
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Abstract
Discrete phase transformations occur in a wide range of structures and systems, from proteins and sub-cellular components in biological systems to micro-scale structures of standard materials. In this paper we study theoretically the mechanical behavior of these intriguing structures. We reexamine the conventional model of a bi-stable chain by introducing the concept of an ideal bi-stable element, and show that any bi-stable element can be conceptually separated into an ideal bi-stable element connected in series with an elastic spring. This new ...
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Abstract
A theoretical analysis is developed for cracked ferroelectric single crystals, focusing on domain switching near the crack tip and field induced crack propagation under a pure electric loading. Domain switching near the crack tip is analyzed first, with the local field concentration determined from the linear piezoelectric fracture analysis, and the resulting domain switching zone established from energetic analysis and compatibility consideration. The crack propagation under a pure electric loading is then analyzed using energy release rate based on field induced ...
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Abstract
Determining the tractions along a surface or interface from measurement data in the far-fields of nonlinear materials is a challenging inverse problem which has significant engineering and nanoscience applications. Previously, a field projection method was established to identify the crack-tip cohesive zone constitutive relations in an isotropic elastic solid (Hong and Kim, 2003. J. Mech. Phys. Solids 51, 1267). In this paper, the field projection method is further generalized to extracting the tractions along interfaces bounded by nonlinear materials, both with ...
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Abstract
Hybrid staggered architecture composites, like nacre and bone, are known for two discernible aspects: superior strength and synergistic toughness. What is lacking is the scientific rationale proving suitability of these materials under impact/time dependent loading. The current investigation aims to address the structure-property correlationship of these materials by development of an analytical model under dynamic rates of loading. Existing literature studies address behavior of staggered materials under quasi-static loading conditions. Critical overlap length was computed for three natural composites-nacre, spider-silk and, ...
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Abstract
Porous metal fiber sintered sheets (MFSSs) are a type of low density cellular materials promising for functional and structural applications. A micromechanics random beam model is proposed to investigate the elasto-plastic behavior of MFSSs. The relative density dependence of the elastic constants and yield strength of MFSSs is predicted and found to agree well with available experimental results. Fiber stretching is identified as the dominant deformation mechanism under uniaxial and multiaxial loading. When compared with two-dimensional Voronoi foams and honeycombs, the ...
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Abstract
Even mild compression can cause re-arrangement of the internal structure of clay-like geomaterials, whereby clusters of particles rotate and collapse as face-to-face contacts between the constituent mineral platelets increase at the expense of edge-to-face (or edge-to-edge) contacts. The collective action of local particle re-orientation ultimately leads to path-independent isochoric macroscopic deformation under continuous shearing. This asymptotic condition is the governing feature of Critical State elasto-plasticity models. Unlike earlier formulations, the two-surface anisotropic model proposed herein is able to reproduce a unique ...
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Abstract
Differential growth of thin elastic bodies furnishes a surprisingly simple explanation of the complex and intriguing shapes of many biological systems, such as plant leaves and organs. Similarly, inelastic strains induced by thermal effects or active materials in layered plates are extensively used to control the curvature of thin engineering structures. Such behaviour inspires us to distinguish and to compare two possible modes of differential growth not normally compared to each other, in order to reveal the full range of out-of-plane ...
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Abstract
The purpose of the research is to describe the swelling-induced large deformations in polymer gels: a theoretical model is developed, and then implemented and solved using the finite element method. The model is firstly assessed with two well-known benchmark problems; moreover, the proposed approach is benchmarked against a recent experiment involving localized exposure of the gel boundary to a solvent, where large bending deformations appear during solvent absorption. In both cases, our results are quite satisfying. ...
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Abstract
Bifurcation theory is often used to investigate the inception of a shear band in a homogeneously deforming body. The theory predicts conjugate shear bands that have the same likelihood of triggering. For structures loaded symmetrically the choice of which of the two conjugate shear bands will persist is arbitrary. In this paper we show that spatial density variation could be a determining factor for the selection of the persistent shear band in a symmetrically loaded localizing sand body. We combine experimental ...
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Abstract
We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model to multilayer graphene materials, including multi-walled carbon nanotubes (MWCNTs). We view the material as a foliation, partitioning of space into a continuous stack of leaves, thus loosing track of the location of the individual graphene layers. The constitutive model for the bulk is derived from the atomistic interactions by appropriate kinematic assumptions, adapted to the foliation structure and mechanics. ...
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Abstract
We present general, computable, improvable, and rigorous bounds for the total energy of a finite heterogeneous volume element Ω or a periodically distributed unit cell of an elastic composite of any known distribution of inhomogeneities of any geometry and elasticity, undergoing a harmonic motion at a fixed frequency or supporting a single-frequency Bloch-form elastic wave of a given wavevector. These bounds are rigorously valid for any consistent boundary conditions that produce in the finite sample or in the unit cell, either ...
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Abstract
We develop a unified framework of balance laws and thermodynamically consistent constitutive equations which couple Cahn–Hilliard-type species diffusion with large elastic–plastic deformations of a body, and account for the swelling and phase segregation caused by the diffusing species. A potential, technologically important, area of application of the theory is in the chemo-mechanical analysis of the evolution of large stresses which develop because of the volume changes associated with the diffusion of lithium ions in the active electrode particles of lithium-ion batteries ...
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Abstract
Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic–matrix composites have not been satisfactorily explained by existing mechanics-based models. In this paper, we use an exact model of fiber fragmentation under global load sharing conditions to predict fracture in three model problems in which non-uniform strains occur: (i) an end-constrained plate subject to a linear transverse temperature gradient; (ii) an internally-pressurized cylindrical tube with a linear through-thickness temperature gradient; and (iii) a rectangular beam under combined bending and tension. Fracture ...
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Abstract
In this work, we present a stress functions approach to include image effects in continuum crystal plasticity arising from the long-range elastic interactions (LRI) between the GND density and free surfaces. The resulting length-scale dependent internal stresses augment those produced by the GND density variation. The formulation is applied to the case of a long, thin specimen subjected to uniform curvature. The analysis shows that under nominally uniform GND density distribution, internal stresses arise from two sources: (1) GND–GND LRI arising ...
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Abstract
We consider a problem of modeling fracture and failure preceded by large scale yielding of ductile shells from the point of view of large-scale structural analysis. We place a special emphasis on the computational efficiency of the constitutive formulation. In this context, we seek the formulation embedded in the shell mechanics framework, which is both theoretically sound and easily implementable into a large-scale explicit dynamic finite element code without precluding vectorization or parallelization. This is achieved through the elasto-plastic damage constitutive ...
|
| |
Abstract
We present a theoretical model to calculate the flexural rigidity of nanowires from three-dimensional elasticity theory that incorporates the effects of surface stress and surface elasticity. The unique features of the model are that it incorporates, through the second moment, the heterogeneous nature of elasticity across the nanowire cross section, and that it accounts for transverse surface-stress-induced relaxation strains. The model is validated by comparison to benchmark atomistic calculations, existing one-dimensional surface elasticity theories based on the Young–Laplace equation, and also ...
|
| |
Abstract
During the past two decades, twinning and slip in hexagonal close-packed structures have been extensively studied using molecular dynamics. However, the simulation methods and corresponding results have rendered different conclusions regarding the active twin modes and their mechanisms for nucleation and growth. The nucleation mechanisms for twinning in hexagonal close-packed polycrystalline materials are known to depend strongly on grain boundary orientations, but little is known of the exact mechanisms that occur. The variability in the experimental behavior of single crystals reported ...
|
| |
Abstract
We present a family of phase-field models for fracture in piezoelectric and ferroelectric materials. These models couple a variational formulation of brittle fracture with, respectively, (1) the linear theory of piezoelectricity, and (2) a Ginzburg–Landau model of the ferroelectric microstructure to address the full complexity of the fracture phenomenon in these materials. In these models, both the cracks and the ferroelectric domain walls are represented in a diffuse way by phase-fields. The main challenge addressed here is encoding various electromechanical crack ...
|
| |
Abstract
A couple stress crystal plasticity formulation that incorporates interfacial couple stress energy was proposed in terms of the virtual work-rate principle for finite element method. By applying the assumed constitutive models of couple stress at the grain boundary as well as the grain interior, finite element simulations were conducted for various crystal models, with different grain subdivision models to examine how plastic deformation work is affected by grain subdivision from the interfacial couple stress energy effect. Finite element simulation results showed ...
|
| |
Abstract
A physically motivated theory of rubber reinforcement based on filler cluster mechanics is presented considering the mechanical behaviour of quasi-statically loaded elastomeric materials subjected to arbitrary deformation histories. This represents an extension of a previously introduced model describing filler induced stress softening and hysteresis of highly strained elastomers. These effects are referred to the hydrodynamic reinforcement of rubber elasticity due to strain amplification by stiff filler clusters and cyclic breakdown and re-aggregation (healing) of softer, already damaged filler clusters. The theory ...
|
| |
Abstract
The steady-state solution for an elastic half-plane under a moving frictionless smooth indenter of arbitrary shape is derived based on the corresponding transient problem and on a condition concerning energy fluxes. Resulting stresses and displacements are found explicitly starting from their expressions in terms of a single analytical function. This solution incorporates all speed ranges, including the super-Rayleigh subsonic and intersonic speed regimes, which received no final description to date. Next, under a similar formulation the wedging of an elastic plane ...
|
| |
Abstract
A phenomenological macroscopic plasticity model is developed for steels that exhibit strain-induced austenite-to-martensite transformation. The model makes use of a stress-state dependent transformation kinetics law that accounts for both the effects of the stress triaxiality and the Lode angle on the rate of transformation. The macroscopic strain hardening is due to nonlinear kinematic hardening as well as isotropic hardening. The latter contribution is assumed to depend on the dislocation density as well as the current martensite volume fraction. The constitutive equations ...
|
| |
Abstract
It is by now well-known that micron-sized metallic crystals exhibit a smaller-being-stronger size effect: the yield strength Ï varies with specimen size D approximately as a power law Ï∼D−m, and the exponent m has been found to vary within a range of ∼0.3 to ∼1.0 for different metals. However, little is known about why such a power law comes into play, and what determines the actual value of the exponent m involved. This work shows that if the yield strength is ...
|
| |
Abstract
A theory for the dynamics and statics of growing elastic rods is presented. First, a single growing rod is considered and the formalism of three-dimensional multiplicative decomposition of morphoelasticity is used to describe the bulk growth of Kirchhoff elastic rods. Possible constitutive laws for growth are discussed and analysed. Second, a rod constrained or glued to a rigid substrate is considered, with the mismatch between the attachment site and the growing rod inducing stress. This stress can eventually lead to instability, ...
|
| |
Abstract
An analytical model of peeling of an elastic tape from a substrate is presented for large deformations and scenarios where sliding occurs in the adhered regions, with this motion resisted by interfacial shear tractions. Two geometries are considered: the first has a free end of the tape being pulled (single-sided peeling), and the second has a detached segment of the tape forming the shape of an inverted letter ‘V’ (double-sided peeling) between adhered sections. The mechanics of peeling is analyzed in ...
|
| |
Abstract
This paper presents a new method for ascertaining residual stress fields in engineering components. Diffraction data are employed with a finite element discretization to determine the macroscopic (continuum) residual stress field over the workpiece simultaneously with the crystal-scale distribution of elastic strains at each diffraction measurement point. Stress equilibrium and traction free boundary conditions constrain the solution at the continuum scale. The thousands of lattice strain measurements made at each diffraction volume ensure that the stress solution is consistent with crystal-scale ...
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Abstract
Microstructure and constituent properties combine to determine the overall fracture toughness of particle-reinforced brittle composites through the activation of different fracture mechanisms. The toughening is through increases in energy dissipation when cracks are forced to follow tortuous paths. Based on the results of numerical simulations, a semi-empirical model is developed to predict the fracture toughness of brittle two-phase ceramic composites as a function of statistically defined morphological attributes of microstructure, constituent properties and interfacial bonding characteristics. The quantification of the fracture ...
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Abstract
New experimental methods are developed to measure the uniaxial power-law creep parameters α and n in the relation ( is the creep strain rate and Ï is the creep stress) from indentation data obtained with a conical or pyramidal indenter. The methods are based on an analysis of Bower et al., which relates the indentation creep rate to the uniaxial creep parameters based on simple assumptions about the constitutive behavior (Bower et al., 1993). Using finite element simulations to establish the ...
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