On the Strain Saturation Conditions for Polycrystalline Ferroelastic Materials

2003 ◽  
Vol 70 (4) ◽  
pp. 470-478 ◽  
Author(s):  
C. M. Landis
Keyword(s):  
Pure Shear ◽  
Micromechanical Model ◽  
Phenomenological Theory ◽  
Internal Variable ◽  
Shear Loading ◽  
Material Behavior ◽  
Constitutive Law ◽  
Tetragonal Crystal ◽  
Self Consistent ◽  
Strain Space

A phenomenological constitutive law is developed for the deformation of polycrystalline ferroelastic materials. The model is framed within a thermodynamic setting common to internal variable plasticity. The two significant inputs to this model are a switching (yield) surface, and a hardening potential. To maintain simplicity, the shape of the switching surface is assumed to be spherical in a modified deviatoric stress space. In order to ascertain the functional form of the hardening potential, micromechanical self-consistent simulations of multiple single crystals, with tetragonal crystal structure, embedded in an effective polycrystalline matrix, are performed for differing loading paths in remanent (plastic) strain space. As a result of the asymmetry in the tension versus compression behavior of these materials, it is shown that pure shear loading does not result in pure shear straining. This feature of the material behavior is demonstrated with the self-consistent simulations and predicted by the phenomenological constitutive law. Ultimately, the phenomenological theory is able to capture the complex constitutive behavior of ferroelastic materials predicted by the micromechanical model.

BI-AXIAL STRESS-STRAIN RELATIONS FOR CONCRETE WITH ISOTROPIC AND ANISOTROPIC DAMAGE

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Siamak Yazdani ◽  
Giuseppe Lomiento ◽  
Yagoub Trad
Keyword(s):  
Damage Mechanics ◽  
Axial Stress ◽  
Confining Pressure ◽  
Internal Variable ◽  
Damage Function ◽  
Material Behavior ◽  
Constitutive Law ◽  
Nonlinear Material ◽  
Variable Theory ◽  
Micro Cracks

For the load paths with small or no confining pressure, the nucleation, growth, and coalescence of cracks and micro-cracks are the main sources of non-linearity in the observed behavior of concrete. The formations of cracks and micro-cracks destroy material bonds and render the material more compliant. These are typically irreversible internal changes and lead to strong directionality in concrete response. To model such nonlinear material behavior, a constitutive law for concrete utilizing damage mechanics is presented for small and isothermal deformations. The general theory is cast within the framework of the internal variable theory of thermodynamics where the dissipation inequality is used. A damage criterion is subsequently obtained using a damage function and the loading-unloading statement is provided. The decomposition of the compliance tensor into damaged and undamaged states is outlined and the flow rules for the inelastic strains are provided. Specific damage response tensors for isotropic and anisotropic modeling is proposed along with numerical simulations that are plotted for illustrating differences between isotropic and anisotropic formulations.

Simplified phenomenological model of the nonlinear behavior of FRPs under combined stress states

2017 ◽  
Vol 52 (4) ◽  
pp. 475-485 ◽  
Author(s):  
Siegfried Galkin ◽  
Fabian J Schirmaier ◽  
Luise Kärger
Keyword(s):  
Shear Stress ◽  
Phenomenological Model ◽  
Pure Shear ◽  
Nonlinear Behavior ◽  
Strain Curve ◽  
Shear Loading ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Combined Stress ◽  
Stress States

Nonlinear material behavior of FRPs under shear loading is widely observed and investigated. In case of combined stress states under tension and shear, an interaction between the macroscopic shear stress–strain curve evolution and the applied tension has been observed and described by several publications in the past. In the present work, the available experimental data with combined stress states are evaluated and a specific threshold shear stress is found, above which nonlinear material behavior occurs for all stress states. Further, a new simplified phenomenological model is derived to model the nonlinear behavior of FRPs when the threshold shear stress is exceeded. This simplified model only needs the threshold shear stress and one evolution parameter, both derived from a pure shear test, to model nonlinear behavior for all combined stress states. A comparison with the available experimental results and with the predictions of the WWFE-III participants for WWFE-III test case 1 shows a very good agreement.

Modeling Creep and Hysteresis in Piezoceramics Using Domain Switching Simulation

2009 ◽  
Author(s):  
Seyed Abdolali Zareian Jahromi ◽  
Qiao Sun
Keyword(s):  
Domain Switching ◽  
Micromechanical Model ◽  
Domain Wall Motion ◽  
Constitutive Law ◽  
Nonlinear Behaviour ◽  
Governing Equations ◽  
Tetragonal Crystal ◽  
Wide Range ◽  
Modeling Creep ◽  
Hysteresis Behaviour

Modeling nonlinear behaviour of polycrystalline piezoceramics accurately can result in an improvement in the wide range of their application, either as actuator or sensor. Two of the main nonlinear behaviours in piezoceramics are hysteresis and creep. These nonlinear and complex macroscopic behaviours of piezoceramics under an electro-mechanical loading are results of domain wall motion in the microscopic level. We developed a micromechanical model to simulate creep and hysteresis behaviour in a piezoceramic. We considered a polycrystal piezoceramic with a random structural configuration of crystals in an isothermal process. An appropriate finite element method (FEM) was used to solve mechanical and electrical governing equations. Each element in FEM represents a crystal in actual polycrystal piezoceramics. volume fractions are needed to evaluate spontaneous polarization and strain caused directly by switching of tetragonal crystal. We improved the constitutive law introduced by Huber et al. [1] in order to consider the effect of exhausted domains in switching process. We used our model to simulate the electromechanical response of a piezoelectric stack under different loading conditions. Our results show a good qualitative agreement with the published experimental results. This model can predict creep as well as hysteresis.

Multiaxial Fatigue of 16MnR Steel

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Zengliang Gao ◽  
Tianwen Zhao ◽  
Xiaogui Wang ◽  
Yanyao Jiang
Keyword(s):  
Pure Shear ◽  
Ambient Air ◽  
Shear Loading ◽  
Multiaxial Fatigue ◽  
Experimental Results ◽  
Pressure Vessel Steel ◽  
Critical Plane ◽  
Cracking Behavior ◽  
Vessel Steel ◽  
Axial Torsion

Uniaxial, torsion, and axial-torsion fatigue experiments were conducted on a pressure vessel steel, 16MnR, in ambient air. The uniaxial experiments were conducted using solid cylindrical specimens. Axial-torsion experiments employed thin-walled tubular specimens subjected to proportional and nonproportional loading. The true fracture stress and strain were obtained by testing solid shafts under monotonic torsion. Experimental results reveal that the material under investigation does not display significant nonproportional hardening. The material was found to display shear cracking under pure shear loading but tensile cracking under tension-compression loading. Two critical plane multiaxial fatigue criteria, namely, the Fatemi–Socie criterion and the Jiang criterion, were evaluated based on the experimental results. The Fatemi–Socie criterion combines the maximum shear strain amplitude with a consideration of the normal stress on the critical plane. The Jiang criterion makes use of the plastic strain energy on a material plane as the major contributor to the fatigue damage. Both criteria were found to correlate well with the experiments in terms of fatigue life. The predicted cracking directions by the criteria were less satisfactory when comparing with the experimentally observed cracking behavior under different loading conditions.

Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

2020 ◽  
Author(s):  
Aref Ghaderi ◽  
Vahid Morovati ◽  
Pouyan Nasiri ◽  
Roozbeh Dargazany
Keyword(s):  
Uncertainty Quantification ◽  
Mechanical Response ◽  
Pure Shear ◽  
Constitutive Models ◽  
Material Behavior ◽  
Elastic Behavior ◽  
Deterministic Models ◽  
Data Set ◽  
Material Parameters ◽  
Axial Extension

Abstract Material parameters related to deterministic models can have different values due to variation of experiments outcome. From a mathematical point of view, probabilistic modeling can improve this problem. It means that material parameters of constitutive models can be characterized as random variables with a probability distribution. To this end, we propose a constitutive models of rubber-like materials based on uncertainty quantification (UQ) approach. UQ reduces uncertainties in both computational and real-world applications. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyper-elastic behavior under different loading conditions (uni-axial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify sensitive parameters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to black-box machine learning approaches that uses data only. In this research, we propagate uncertainty through the model, characterize sensitivity of material behavior to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical response of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uni-axial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.

Loading Direction Versus Crack Propagation Path in a Lead-Free Single Solder Joint Sample

2008 ◽  
Author(s):  
Feng Gao ◽  
Jianping Jing ◽  
Janine Johnson ◽  
Frank Z. Liang ◽  
Richard L. Williams ◽  
...  
Keyword(s):  
Solder Alloy ◽  
Mixed Mode ◽  
Shear Fracture ◽  
Pure Shear ◽  
Shear Loading ◽  
Propagation Path ◽  
Mixed Mode Loading ◽  
Cohesive Failure ◽  
Loading Direction ◽  
Shear Component

In this paper, single solder joints (SSJs) were subjected to moderate speed loading (5mm/sec) in different directions, from pure tensile, mixed mode to pure shear. Fracture surfaces from different loading directions were examined both experimentally and numerically. It is observed that intermetallic compound (IMC) is formed between the solder alloy and the Cu pad, and failure typically occurs at or near the solder/IMC/Cu interfaces on the board side. Pure tensile loading typically leads to interfacial fracture along the IMC/Cu interface. Mixed mode loading usually results in a mixture of interfacial and cohesive failure with crack propagating in a zigzag fashion between the solder/IMC interface and the solder alloy. Loading with higher shear component tends to result in more cohesive failure of the solder alloy near the solder/IMC interface. Under pure shear loading, failure is almost always cohesive within the solder alloy near the solder/IMC interface.

Dynamic Stability of Unidirectional Fiber-Reinforced Viscoelastic Composite Plates

1989 ◽  
Vol 42 (11S) ◽  
pp. S39-S47 ◽  
Author(s):  
N. K. Chandiramani ◽  
L. Librescu
Keyword(s):  
Shear Deformation ◽  
Dynamic Stability ◽  
Stability Problem ◽  
Micromechanical Model ◽  
Shear Deformation Theory ◽  
Constitutive Law ◽  
Fiber Reinforced ◽  
Viscoelastic Composite ◽  
Unidirectional Fiber ◽  
The Stability

This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a 3-D viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi’s micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.

A Phenomenological Theory of Aging Effects of Metals

1973 ◽  
Vol 95 (2) ◽  
pp. 107-111 ◽  
Author(s):  
D. C. Stouffer ◽  
A. M. Strauss
Keyword(s):  
Time Domain ◽  
Perturbation Technique ◽  
Phenomenological Theory ◽  
Constitutive Law ◽  
Strain History ◽  
Arc Length ◽  
Aging Effects ◽  
Aging Properties ◽  
Theory Of Aging ◽  
The Time Domain

A constitutive law is developed for metals which have aging properties. The development of this law is based on the assumption that the mechanical properties of simple aging materials can be mathematically represented by a functional of the strain history, and that this functional depends upon the age of the material. A perturbation technique allows the separation of the nonaging response from the aging effects, and leads to convenient representations for viscoelasticity and plasticity. The mechanical behavior of aging metals is studied by applying the arc length parameterization of the strain history. The final rate independent results are transformed to the time domain for efficient use in engineering applications and in solving boundary value problems.

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