A Large Deformation Plasticity Model With Rate Sensitivity and Thermal Softening

1984 ◽  
Vol 106 (4) ◽  
pp. 388-392
Author(s):  
D. W. Nicholson ◽  
K. C. Kiddy
Keyword(s):  
Large Deformation ◽  
Shear Banding ◽  
Small Deformation ◽  
Rate Sensitivity ◽  
Thermal Softening ◽  
Dynamic Loads ◽  
Extended Model ◽  
Adiabatic Shear Banding ◽  
Deformation Plasticity ◽  
Applied Stresses

In this paper, a previously published small deformation constitutive model with rate sensitive plasticity and thermal softening is extended to large deformation. The extended model appears suitable for describing a deleterious thermoplastic process manifested by adiabatic shear banding in materials such as titanium under severe dynamic loads. The nature of the instability admitted by the model is described. Also, calculations are reported on the rapid extension of a titanium strip. For applied stresses several times the yield stress, a deleterious temperature is attained in times of the order of 10−2 s.

The Role of Rate Effects and of Thermomechanical Coupling in Shear Localization

1997 ◽  
Vol 119 (4) ◽  
pp. 322-331 ◽  
Author(s):  
Y. Estrin ◽  
A. Molinari ◽  
S. Mercier
Keyword(s):  
Numerical Simulations ◽  
Strain Localization ◽  
Mechanical Energy ◽  
Shear Banding ◽  
Rate Sensitivity ◽  
Thermomechanical Coupling ◽  
Face Centered Cubic ◽  
Adiabatic Shear Banding ◽  
Thin Walled Tube ◽  
Face Centered

A dislocation density related constitutive model that accounts for the strain-rate sensitivity of the flow stress and, notable, of the strain-hardening coefficient was applied to describe adiabatic shear banding in face centered cubic metals. The parameter values of a prototype material, for which numerical simulations were carried out, are close to those of copper. The effect of the material parameters, especially of those reflecting the two rate sensitivities, on the occurrence of strain localization in a thin-walled tube under torsion containing a geometrical defect was investigated systematically. The results obtained provide some guidance with respect to design of materials with high resistance to strain localization and high mechanical energy absorption. Another outcome of this study is the recognition that for the problem in question linear stability analysis cannot provide a reliable criterion even for the onset of strain localization, and that numerical simulations have to be invoked.

Shear Stability, Instability and Localization of Materials Exhibiting Thermal Softening, Strain Rate Sensitivity and Strain Hardening

1989 ◽  
Vol 111 (4) ◽  
pp. 250-253 ◽  
Author(s):  
N. Charalambakis
Keyword(s):  
Test Problem ◽  
Shear Banding ◽  
Homogeneous Solution ◽  
Rate Sensitivity ◽  
Thermal Softening ◽  
Simple Shearing ◽  
Shear Forces ◽  
Localization Of Plastic Deformation ◽  
Dependent Flow

We consider the test-problem of simple shearing of a thermoviscoplastic solid subject to steady or time-dependent boundary velocities or shear forces. Previously derived stability and nonlocalization criteria are presented. The influence of boundary conditions on the time-asymptotic “solution,” the role of nonuniformities and the localization of plastic deformation are discussed. Finally, a perturbation analysis of homogeneous solution under steady boundary velocities or stresses of a material with a gradient-dependent flow stress is presented and “shear-banding” criteria are derived.

Mechanical properties of the tadpole tail fin

1998 ◽  
Vol 201 (19) ◽  
pp. 2691-2699 ◽  
Author(s):  
PA Doherty ◽  
RJ Wassersug ◽  
JM Lee
Keyword(s):  
Stress Relaxation ◽  
Large Deformation ◽  
Forced Vibration ◽  
Viscoelastic Properties ◽  
Developmental Plasticity ◽  
Rana Catesbeiana ◽  
Small Deformation ◽  
Collagen Fibres ◽  
Tadpole Tail ◽  
Undulatory Swimming

The tadpole tail fin is a simple double layer of skin overlying loose connective tissue. Collagen fibres in the fin are oriented at approximately +/-45 degrees from the long axis of the tail. Three tests were conducted on samples of the dorsal tail fin from 6-10 Rana catesbeiana tadpoles to establish the fin's viscoelastic properties under (1) large-deformation cyclic loading at 1 and 3 Hz, (2) small-deformation forced vibration at 1 and 3 Hz, and (3) stress relaxation under a 0.1 s loading time. The fin was very fragile, failing easily under tensile loads less than 7 g. It was also strikingly viscoelastic, as demonstrated by 72+/-1 % hysteresis loss (at 3 Hz), 16+/-3 % stress remaining after 100 s of stress relaxation and a phase angle of 18+/-1 degrees in forced vibration. As a consequence of its viscoelastic properties, the fin was three times stiffer in small than in large deformation. This may account for the ability of the fin to stay upright during normal undulatory swimming, despite the absence of any skeletal support. Tadpoles in nature are often found with damaged tails. We suggest that the unusually viscoelastic and fragile nature of the fin helps tadpoles escape the grasp of predators. Because the fin deforms viscoelastically and tears easily, tadpoles can escape predators and survive otherwise lethal attacks with only minor lacerations to the fin. Recent studies have shown that certain tadpoles develop taller fins in the presence of predators. This developmental plasticity is consistent with the tail fin acting as a protective but expendable 'wrap' around the core muscle tissue.

Test of Strain-Time Correspondence Principle with Gel-Containing Elastomers

1986 ◽  
Vol 59 (2) ◽  
pp. 305-314 ◽  
Author(s):  
N. Nakajima ◽  
E. R. Harrell
Keyword(s):  
Large Deformation ◽  
Correspondence Principle ◽  
Small Deformation ◽  
Complex Viscosity ◽  
Shear Stresses ◽  
Growth Data ◽  
Stress Growth ◽  
Linear Viscoelastic ◽  
The Difference ◽  
Linear Viscoelastic Theory

Abstract With four NBR samples and one EPR, oscillatory measurements and stress-growth measurements were performed, the former being at very small deformation and the latter leading to large deformation. The Rheometrics mechanical spectrometer was used with a cone-plate fixture. The temperature was 100°C. The stress-growth data of NBR's, converted to complex viscosity-frequency data through the application of stress-time correspondence principle, were in good agreement with those observed in the oscillatory measurement. Thus, the stress-growth data including the large deformation were “linearized” to form a master curve. With the EPR sample, such a linearization was not necessary. The stress-growth data were adequately treated with the linear viscoelastic theory up to shear stresses approaching the steady state. The difference in behavior between the NBR's and EPR is caused by differences in type and extent of long branching and gel present in the samples.

A constitutive model for anisotropic, kinematic hardening materials

1997 ◽  
Vol 32 (3) ◽  
pp. 175-181
Author(s):  
W Deng ◽  
A Asundi ◽  
C W Woo
Keyword(s):  
Inelastic Deformation ◽  
Internal State ◽  
Kinematic Hardening ◽  
Small Deformation ◽  
Inelastic Strain ◽  
State Variables ◽  
Internal State Variables ◽  
Deformation Plasticity ◽  
Independent Variable ◽  
Evolution Laws

Based on previous work by the authors, a model for anisotropic, kinematic hardening materials is constructed to describe constitutive equations and evolution laws in rate-independent, small deformation plasticity on the basis of thermodynamics. Unlike other theories developed earlier wherein only internal state variables are chosen to describe inelastic deformation, the present paper also considers inelastic strain as an independent variable. This can be shown to reduce to the well-known plastic strain in the case of rate-independent plasticity.

scholarly journals On the Quantitative Evaluation of Adiabatic Shear Banding Sensitivity of Various Titanium Alloys

1997 ◽  
Vol 07 (C3) ◽  
pp. C3-429-C3-434 ◽  
Author(s):  
C. Mazeau ◽  
L. Beylat ◽  
P. Longère ◽  
P. F. Louvigné
Keyword(s):  
Titanium Alloys ◽  
Quantitative Evaluation ◽  
Shear Banding ◽  
Adiabatic Shear ◽  
Adiabatic Shear Banding
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