Improved Constitutive Equations for Modeling Strain Softening—Part I: Conceptual Development

1984 ◽  
Vol 106 (4) ◽  
pp. 337-342 ◽  
Author(s):  
T. C. Lowe ◽  
A. K. Miller
Keyword(s):  
Constitutive Equations ◽  
Work Hardening ◽  
Short Range ◽  
Conceptual Development ◽  
Strain Softening ◽  
Dynamic Recovery ◽  
Internal Stresses ◽  
Wide Range ◽  
Deformation Behaviors ◽  
Heterogeneous Microstructures

A microstructurally based model of nonelastic deformation is proposed which is capable of predicting strain softening as well as a wide range of other deformation behaviors. The model, an extension of the MATMOD constitutive equations, now includes representations of both short range and long range internal stresses, strengthening due to homogeneous and heterogeneous microstructures, and dynamic recovery. Additional conceptual improvements regarding the interactions between various sources of work hardening and the influence of straining direction upon deformation induced microstructures are also introduced. The physical origins of these extensions, their relationship to strain softening, and their implementation in the new model, MATMOD-4V, are presented.

Improved Constitutive Equations for Modeling Strain Softening—Part II: Predictions for Aluminum

1984 ◽  
Vol 106 (4) ◽  
pp. 343-348 ◽  
Author(s):  
T. C. Lowe ◽  
A. K. Miller
Keyword(s):  
High Purity ◽  
Constitutive Equations ◽  
Strain Softening ◽  
Substantial Improvement ◽  
Deformation Model ◽  
Independent Data ◽  
Model Predictions ◽  
Deformation Behaviors ◽  
High Purity Aluminum

The capabilities of a new deformation model, MATMOD-4V, are demonstrated by comparison of computer predictions against independent data for high purity aluminum. In particular, model predictions of strain softening are presented and discussed. The predictive abilities of MATMOD-4V represent a substantial improvement over earlier versions of the MATMOD constitutive equations. The strength of the approach is illustrated by MATMOD-4V’s ability to predict deformation behaviors not explicitly built into the model.

Modeling Internal Stresses in the Nonelastic Deformation of Metals

1986 ◽  
Vol 108 (4) ◽  
pp. 365-373 ◽  
Author(s):  
T. C. Lowe ◽  
A. K. Miller
Keyword(s):  
Experimental Data ◽  
Long Range ◽  
Cyclic Deformation ◽  
Deformation Behavior ◽  
Short Range ◽  
Dynamic Recovery ◽  
Small Strain ◽  
Internal Stresses ◽  
Deformation Model

The roles of short range and long range internal stresses during nonelastic deformation have been postulated and explored using the MATMOD-4V deformation model. New microstructural variables have been introduced in MATMOD-4V which represent the effects of internal stresses upon deformation. Simulations for aluminum have been performed to demonstrate improved capability to represent small strain deformation behavior and dynamic recovery. Comparisons are made between experimental data and computer predictions of microplastic straining and cyclic deformation.

scholarly journals Dynamic Recrystallization Critical Conditions and a Physically–Based Constitutive Model of Al–4.8Mg Alloy Under Hot Working Conditions

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4982 ◽  
Author(s):  
Qingsong Dai ◽  
Yunlai Deng ◽  
Yu Wang ◽  
Wenhui Huang
Keyword(s):  
Constitutive Model ◽  
Dynamic Recrystallization ◽  
Process Parameters ◽  
Work Hardening ◽  
Dynamic Recovery ◽  
Critical Conditions ◽  
Compression Tests ◽  
Absolute Relative Error ◽  
Average Absolute Relative Error ◽  
Wide Range

The microstructure evolution and the mechanical behavior of Al–4.8Mg alloy were investigated by means of isothermal compression tests at various temperatures (280–520 °C) and strain rates (0.01–10 s−1). The results shown that there are three main mechanisms of dynamic softening of samples within the range of selected process parameters: dynamic recovery, dynamic recovery + dynamic recrystallization, and dynamic recrystallization, and the equiaxed dynamic recrystallization grain tends to be formed under higher temperature and higher strain rate. In order to accurately describe the dynamic recrystallization condition of Al-4.8Mg alloy under a wide range of hot deformation parameters, an improved dynamic recrystallization critical conditions model is proposed based on deformation activation energy and work-hardening rate. Additionally, a two–stage physically constitutive model considering the influence of work hardening–dynamic recovery and dynamic recrystallization is established. Comparisons between the predicted and experimental data indicate that the proposed model can adequately predict the flow stress in the range of selected process parameters with the average absolute relative error of 4.02%.

Theoretical study of the prestressing strand's stress by computer modeling methods

2020 ◽  
Vol 76 (11) ◽  
pp. 1139-1148
Author(s):  
A. G. Korchunov ◽  
E. M. Medvedeva ◽  
E. M. Golubchik
Keyword(s):  
Residual Stresses ◽  
High Strength ◽  
Pearlitic Steel ◽  
Internal Stresses ◽  
Steel Microstructure ◽  
Compressive Stresses ◽  
Wide Range ◽  
Prestressing Strands ◽  
Increasing Temperature ◽  
Wire Strand

The modern construction industry widely uses reinforced concrete structures, where high-strength prestressing strands are used. Key parameters determining strength and relaxation resistance are a steel microstructure and internal stresses. The aim of the work was a computer research of a stage-by-stage formation of internal stresses during production of prestressing strands of structure 1х7(1+6), 12.5 mm diameter, 1770 MPa strength grade, made of pearlitic steel, as well as study of various modes of mechanical and thermal treatment (MTT) influence on their distribution. To study the effect of every strand manufacturing operation on internal stresses of its wires, the authors developed three models: stranding and reducing a 7-wire strand; straightening of a laid strand, stranding and MTT of a 7-wire strand. It was shown that absolute values of residual stresses and their distribution in a wire used for strands of a specified structure significantly influence performance properties of strands. The use of MTT makes it possible to control in a wide range a redistribution of residual stresses in steel resulting from drawing and strand laying processes. It was established that during drawing of up to 80% degree, compressive stresses of 1100-1200 MPa degree are generated in the central layers of wire. The residual stresses on the wire surface accounted for 450-500 MPa and were tension in nature. The tension within a range of 70 kN to 82 kN combined with a temperature range of 360-380°С contributes to a two-fold decrease in residual stresses both in the central and surface layers of wire. When increasing temperature up to 400°С and maintaining the tension, it is possible to achieve maximum balance of residual stresses. Stranding stresses, whose high values entail failure of lay length and geometry of the studied strand may be fully eliminated only at tension of 82 kN and temperature of 400°С. Otherwise, stranding stresses result in opening of strands.

Rate Dependent Constitutive Equations of Cyclic Softening

1985 ◽  
Vol 40 (7) ◽  
pp. 653-665
Author(s):  
J. S. Mshana ◽  
A. S. Krausz
Keyword(s):  
Stress Relaxation ◽  
Low Temperature ◽  
Constitutive Equations ◽  
Strain Softening ◽  
Structural Characteristics ◽  
High Stress ◽  
Cyclic Strain ◽  
Cyclic Stress ◽  
Cyclic Softening ◽  
Stress Softening

Constitutive equations of cyclic strain and stress softening for materials with low internal stress levels are derived from the rate theory. The study shows that over the high stress and low temperature range where the description of plastic flow in cyclic softening can be approximated with activation over a single energy barrier, cyclic strain softening is well related to stress relaxation process while cyclic stress softening is related to creep process. The material structural characteristics for cyclic strain softening, cyclic stress softening and stress relaxation are identical. Subsequently, it is shown that cyclic stress and strain softening within the high stress and low temperature range can be evaluated from the constitutive equations using the material structural characteristics measured from a simple stress relaxation test.

Rolling and Recrystallization Textures in High Purity Al Cold Rolled to Very High Rolling Reductions

2005 ◽  
Vol 495-497 ◽  
pp. 603-608 ◽  
Author(s):  
Atsushi Todayama ◽  
Hirosuke Inagaki
Keyword(s):  
Cold Rolling ◽  
High Purity ◽  
Work Hardening ◽  
Dynamic Recovery ◽  
The Other ◽  
Rolling Reduction ◽  
Theoretical Investigations ◽  
Theoretical Predictions ◽  
Cold Rolled ◽  
Very High

On the basis of Taylor-Bishop-Hill’s theory, many previous theoretical investigations have predicted that, at high rolling reductions, most of orientations should rotate along theβfiber from {110}<112> to {123}<634> and finally into the {112}<111> stable end orientations. Although some exceptions exist, experimental observations have shown, on the other hand, that the maximum on the β fiber is located still at about {123}<634> even after 97 % cold rolling. In the present paper, high purity Al containing 50 ppm Cu was cold rolled up to 99.4 % reduction in thickness and examined whether {112}<111> stable end orientation could be achieved experimentally. It was found that, with increasing rolling reduction above 98 %, {110}<112> decreased, while orientations in the range between {123}<634> and {112}<111> increased, suggesting that crystal rotation along the βfiber from {110}<112> toward {123}<634> and {112}<111> in fact took place. At higher rolling reductions, however, further rotation of this peak toward {112}<111> was extremely sluggish, and even at the highest rolling reduction, it could not arrive at {112}<111>. Such discrepancies between theoretical predictions and experimental observations should be ascribed to the development of dislocation substructures, which were formed by concurrent work hardening and dynamic recovery. Since such development of dislocation substructures are not taken into account in Taylor-Bishop-Hill’s theory, it seems that they can not correctly predict the development of rolling textures at very high rolling reductions, i. e. stable end orientations. On annealing specimens rolled above 98 % reduction in thickness, cube textures were very weak, suggesting that cube bands were almost completely rotated into other orientations during cold rolling. {325}<496>, which lay at an intermediate position between {123}<634> and {112}<111> along theβfiber, developed strongly in the recrystallization textures.

Hypo-elasticity and plasticity

1956 ◽  
Vol 234 (1196) ◽  
pp. 46-59 ◽  
Keyword(s):  
General Theory ◽  
Constitutive Equations ◽  
Work Hardening ◽  
Strain Curve ◽  
Simple Extension ◽  
Logarithmic Strain ◽  
Elasticity Equations ◽  
Plastic Materials ◽  
Special Case

A general theory of work-hardening incompressible plastic materials is developed as a special case of Truesdell’s theory of hypo-elasticity. Equations are given in general coordinates for a single loading followed by one unloading, and attention is directed to materials for which the stress-logarithmic strain curve for unloading in simple extension is linear. Using a particular case of the corresponding constitutive equations for loading, which is a generalization of that suggested by Prager, applications are made to a number of specific problems.

The Work Hardening of Single Phase and Multi-Phase Aluminium Alloys

2006 ◽  
Vol 519-521 ◽  
pp. 71-78 ◽  
Author(s):  
J. David Embury ◽  
Warren J. Poole ◽  
David J. Lloyd
Keyword(s):  
Work Hardening ◽  
Aluminium Alloys ◽  
Single Phase ◽  
Dynamic Recovery ◽  
Uniform Elongation ◽  
Strengthening Mechanisms ◽  
Plastic Response ◽  
Spring Back ◽  
Hardening Process ◽  
Multi Phase

The process of work hardening in aluminum alloys is important from the viewpoint of formability and the prediction of the properties of highly deformed products. However the complexity of the strengthening mechanisms in these materials means that one must carefully consider the interaction of dislocations with the detailed elements of the microstructure and the related influence of the elements on dislocation accumulation and dynamic recovery. In addition, it is necessary to consider the influence of the work hardening process at various levels of plastic strain. This permits the possibility of designing microstructure for tailored plastic response, e.g. not simply designed for yield strength but also considering uniform elongation, spring-back, ductility etc. This presentation will explore the concept of identifying the various interactions which govern the evolution of the work hardening and their possible role in alloy design.

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