A Viscoplastic Constitutive Theory for Monolithic Ceramics — II

1999 ◽  
Author(s):  
Lesley A. Janosik ◽  
Stephen F. Duffy
Keyword(s):  
Hydrostatic Stress ◽  
Rate Sensitivity ◽  
Time Dependent ◽  
Homogeneous State ◽  
Computer Algorithms ◽  
Load History ◽  
Deformation Response ◽  
Service Load ◽  
Tension And Compression ◽  
Monolithic Ceramics

This paper, which is the second of two in a series, exercises the viscoplastic constitutive model developed by the authors in the previous article (Janosik and Duffy, 1998). The model accounts for time-dependent phenomena (e.g., creep, rate sensitivity, and stress relaxation) in monolithic ceramics. Additionally, the formulation exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression. Here, the constitutive equations formulated for the flow law (i.e., the Strain rate) and the evolutionary law have been incorporated into computer algorithms for predicting the multiaxial inelastic (creep) response of a given homogeneous state of stress. Numerically simulated examples illustrate the model’s ability to capture the time-dependent phenomena suggested above. For each imposed service (load) history considered, creep curves and viscoplastic flow surfaces are examined to demonstrate the model’s ability to capture the inelastic creep deformation response. No attempt is made here to assess the accuracy of the model in comparison to experiment. A quantitative assessment is reserved for a later date, after the material constants have been suitably characterized for a specific ceramic material.

A Viscoplastic Constitutive Theory for Monolithic Ceramics—I

1998 ◽  
Vol 120 (1) ◽  
pp. 155-161 ◽  
Author(s):  
L. A. Janosik ◽  
S. F. Duffy
Keyword(s):  
Potential Function ◽  
Constitutive Equations ◽  
Hydrostatic Stress ◽  
Functional Dependence ◽  
Threshold Function ◽  
Cauchy Stress ◽  
Creep Stress ◽  
Flow Potential ◽  
Tension And Compression ◽  
Monolithic Ceramics

This paper, which is the first of two in a series, provides an overview of a viscoplastic constitutive model that accounts for time-dependent material deformation (e.g., creep, stress relaxation, etc.) in monolithic ceramics. Using continuum principles of engineering mechanics, the complete theory is derived from a scalar dissipative potential function first proposed by Robinson (1978), and later utilized by Duffy (1988). Derivations based on a flow potential function provide an assurance that the inelastic boundary value problem is well posed, and solutions obtained are unique. The specific formulation used here for the threshold function (a component of the flow potential function) was originally proposed by Willam and Warnke (1975) in order to formulate constitutive equations for time-independent classical plasticity behavior observed in cement and unreinforced concrete. Here constitutive equations formulated for the flow law (strain rate) and evolutionary law employ stress invariants to define the functional dependence on the Cauchy stress and a tensorial state variable. This particular formulation of the viscoplastic model exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression.

scholarly journals A Viscoplastic Constitutive Theory for Monolithic Ceramics: I

1996 ◽  
Author(s):  
Lesley A. Janosik ◽  
Stephen F. Duffy
Keyword(s):  
Potential Function ◽  
Constitutive Equations ◽  
Hydrostatic Stress ◽  
Functional Dependence ◽  
Threshold Function ◽  
Cauchy Stress ◽  
Creep Stress ◽  
Flow Potential ◽  
Tension And Compression ◽  
Monolithic Ceramics

This paper, which is the first of two in a series, provides an overview of a viscoplastic constitutive model that accounts for time-dependent material deformation (e.g., creep, stress relaxation, etc.) in monolithic ceramics. Using continuum principles of engineering mechanics the complete theory is derived from a scalar dissipative potential function first proposed by Robinson (1978), and later utilized by Duffy (1988). Derivations based on a flow potential function provide an assurance that the inelastic boundary value problem is well posed, and solutions obtained are unique. The specific formulation used here for the threshold function (a component of the flow potential function) was originally proposed by Willam and Warnke (1975) in order to formulate constitutive equations for time-independent classical plasticity behavior observed in cement and unreinforced concrete. Here constitutive equations formulated for the flow law (strain rate) and evolutionary law employ stress invariants to define the functional dependence on the Cauchy stress and a tensorial state variable. This particular formulation of the viscoplastic model exhibits a sensitivity to hydrostatic stress, and allows different behavior in tension and compression.

Creep of thermoplastics under uniaxial, shear, and hydrostatic stress conditions

1973 ◽  
Vol 8 (4) ◽  
pp. 277-285 ◽  
Author(s):  
P P Benham ◽  
P J Mallon
Keyword(s):  
Hydrostatic Stress ◽  
Strain Ratio ◽  
Hydrostatic Compression ◽  
Time Dependent ◽  
Creep Data ◽  
Volume Strain ◽  
Linear Elastic ◽  
Uniaxial Creep ◽  
Simple Tension ◽  
Tension And Compression

Creep data obtained from p.v.c., p.m.m.a., and p.p. sheet in uniaxial tension and compression, shear, and hydrostatic compression were used to test analytical correlating procedures. It was shown that shear and uniaxial creep could be closely related through the concept of shear stress and shear strain on octahedral planes. Volume strain in uniaxial creep was expressed in terms of the co-ordinate strains and used to predict volume strain in hydrostatic compression. These correlating procedures were only effective if due allowance was made for the different creep responses in simple tension and compression for each of these materials. It was also shown that the relations between viscoelastic compliances and strain ratio, which are stress- and time-dependent, have the same form as the relations between the linear elastic constants.

An Incremental Criterion for Time-Dependent Failure of Materials

1976 ◽  
Vol 98 (2) ◽  
pp. 140-145 ◽  
Author(s):  
S. R. Bodner ◽  
U. S. Lindholm
Keyword(s):  
Failure Criterion ◽  
Strain Energy ◽  
Hydrostatic Stress ◽  
Time Dependent ◽  
Accumulation Of Damage ◽  
The Mean ◽  
Flow Law ◽  
Dependent Failure

A criterion for the time-dependent failure of materials is developed based upon the concept that failure results from an incremental accumulation of damage. The failure criterion is thereby explicitly tied to the incremental flow law describing the inelastic deformations. The damage increment is assumed as a product of functions of the stored strain energy due to inelastic deformations, the mean hydrostatic stress, and the damage itself. The consequences of the failure criterion for various types of loading are discussed.

Fracture Behavior of Ultrafine-Grained Titanium Under Tension at Elevated Temperatures

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
S. V. Sajadifar ◽  
H. J. Maier ◽  
T. Niendorf ◽  
G. G. Yapici
Keyword(s):  
Fracture Behavior ◽  
Elevated Temperatures ◽  
Rate Sensitivity ◽  
Void Coalescence ◽  
Strain Rates ◽  
Enhanced Diffusion ◽  
Deformation Response ◽  
Ultrafine Grained ◽  
Highly Sensitive ◽  
Comprehensive Recovery

Abstract This investigation focused on the deformation response and microstructural changes of severely deformed titanium during post-severe plastic deformation tension, at temperatures of 300–600 °C and at strain rates of 0.001–0.1 s−1. The obtained results suggest that SPD enhances the strength of grade 4 titanium up to 500 °C. At above 600 °C, the severely deformed microstructure showed comprehensive recovery. Severely deformed titanium was seen to be highly sensitive to the deformation rate, where strain rate sensitivity increased with the increase of test temperature. Analysis of fracture surfaces reveals that at elevated temperatures, growth of dimples and void coalescence occurs due to the enhanced diffusion rate and occurrence of recrystallized grains.

A Model for the Effects of Strain Rate and Temperature on the Deformation Behavior of Ultrafine-Grained Metals

2011 ◽  
Vol 291-294 ◽  
pp. 1173-1177
Author(s):  
Zi Ling Xie ◽  
Lin Zhu Sun ◽  
Fang Yang
Keyword(s):  
Grain Boundary ◽  
Strain Rate ◽  
Deformation Behavior ◽  
Boundary Diffusion ◽  
Rate Sensitivity ◽  
Grain Boundary Sliding ◽  
Dislocation Slip ◽  
Deformation Response ◽  
Ultrafine Grained ◽  
Boundary Sliding

A theoretical model is developed to account for the effects of strain rate and temperature on the deformation behavior of ultrafine-grained fcc Cu. Three mechanisms, including dislocation slip, grain boundary diffusion, and grain boundary sliding are considered to contribute to the deformation response simultaneously. Numerical simulations show that the strain rate sensitivity increases with decreasing grain size and strain rate, and that the flow stress and tensile ductility increase with either increasing strain rate or decreasing deformation temperature.

THE STABILITY OF FCC CRYSTAL Cu UNDER UNIAXIAL LOADING IN [001] DIRECTION

2009 ◽  
Vol 23 (15) ◽  
pp. 1871-1880 ◽  
Author(s):  
X. M. LIU ◽  
Z. L. LIU ◽  
X. C. YOU ◽  
J. F. NIE ◽  
Z. ZHUANG
Keyword(s):  
Hydrostatic Stress ◽  
Element Model ◽  
Uniaxial Loading ◽  
Ideal Strength ◽  
Anisotropic Character ◽  
Tension And Compression ◽  
Loading Tests ◽  
The Stability ◽  
Critical Resolved Shear Stress ◽  
The Ideal

Uniaxial loading tests of copper with inter-atomic potential finite-element model are carried out to determine the corresponding ideal tension and compression strength using the modified Born stability criteria. The influence of biaxial stresses applied perpendicularly to the [100] loading axis, on the ideal strength is investigated, and tension-compression asymmetry in ideal strength under [100] loading is also studied. The results suggest that asymmetry for yielding strength of [100] nanowires may result from anisotropic character of crystal instability. Moreover, the results also reveal that the critical resolved shear stress in the direction of slip is not an accurate criterion for the ideal strength since it cannot capture the dependence on the loading conditions and hydrostatic stress components for the ideal strength.

scholarly journals Yield Stress Anomaly in B2 FeAl

1996 ◽  
Vol 460 ◽  
Author(s):  
K. Yoshimi ◽  
S. Hanada ◽  
M. H. Yoo
Keyword(s):  
Single Crystals ◽  
Yield Stress ◽  
Rate Sensitivity ◽  
Recovery Process ◽  
Peak Temperature ◽  
Positive Temperature ◽  
Slip Vector ◽  
Temperature Range ◽  
Tension And Compression ◽  
Increasing Temperature

ABSTRACTOur studies on yield stress anomaly of B2 FeAI single crystals are reviewed in this paper. A positive temperature dependence of yield stress, so-called “yield stress anomaly”, is observed in B2 FeAI in which excess vacancies are fully annealed out. Associated with the anomaly, characteristic asymmetry is found between tension and compression. While the strain-rate sensitivity is almost zero in the temperature range of the yield stress anomaly, the stress relaxation becomes significant with increasing temperature, indicating that a recovery process is thermally activated. It is ascertained by the two-surface trace analysis that slip transition from <111> direction at intermediate temperature to <100> at high temperature occurs around the peak temperature. Even at the peak temperature, in addition, operative slip vector for yielding is confirmed to be predominantly <111> by TEM. Also, it is observed that <111>-type superdislocations are frequently climb-dissociated in the temperature range of the anomaly. APB formation on {111} plane is energetically favorable, which is in agreement with the Flinn's calculation for the B2 superlattice that APB energy on {111} plane is lower than that on {110} plane. Such an anisotropy of APB energy would offer specific driving force for the climb dissociation on <111> superdislocations. On the basis of the observed results, the anomalous strengthening behavior of B2 FeAI single crystals is discussed.

A Mechanical Material Model for Aluminium Extrusions During On-line Quenching

1996 ◽  
Vol 118 (1) ◽  
pp. 114-119 ◽  
Author(s):  
Niklas Ja¨rvstra˚t ◽  
Stig Tjo̸tta
Keyword(s):  
Mechanical Behaviour ◽  
Room Temperature ◽  
Material Model ◽  
Load History ◽  
Single Test ◽  
Experimental Procedure ◽  
Material Parameters ◽  
Continuous Cooling ◽  
Tension And Compression ◽  
On Line

A material model is suggested, suitable for modelling the mechanical behaviour of aluminium sections, from directly after the extrusion and throughout the on-line quenching to room temperature. An experimental procedure is detailed, whereby all material parameters in the model can be determined by a single test. In the test, the specimen is subjected to a carefully prescribed load history in tension and compression during continuous cooling. Material parameters are determined for the AIMgSi alloy AA6060. Finally, the model is compared with conventional plasticity and viscoplasticity, and found to give much better accuracy.

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