scholarly journals Material Similarity of Scaled Models

Author(s):  
Shuai Wang ◽  
Fei Xu ◽  
Xiaoyu Zhang ◽  
Leifeng Yang

When different strain hardening and strain rate sensitive materials are used for scaled model and prototype, the traditional pure geometrical similarity laws of solid mechanics will fail. Although correcting the basic scaling factors of velocity, density and geometry have been developed to compensate for the material distortion in recent non-geometric scaling works, it is difficult to be widely used because of its inherent indirect (depending on the structural strain and strain rate responses) and inexact (having significant prediction errors for prototype) defects. In this paper, a framework of material similarity, based on the new suggested material dimensionless numbers and the ‘Material number vs. strain/strain-rate’ function curves, are further developed, which represents the objective requirement of similarity theory for the basic mechanical properties of materials. It is demonstrated what is similitude materials of solid mechanics and how to use the best similitude materials to overcome the non-scalabilities of materials for identical or different materials. The direct and exact solution of the basic correction factors is further obtained and therefore overcomes the previous inherent indirect and inexact defects radically. Based on the similarity evaluation of different materials of the classical constitutive models, the impacted structures of circular plate and crooked plate with strain hardening and strain rate sensitive materials are verified numerically. The results show the completely different materials can be exact similitude for various structural behaviors (strain, strain rate, stress and displacement) of time and space fields after using the best similitude materials; and the basic correction factors do not depend on the structural strain and strain rate responses. As a contrast, when the non-similitude materials are used, the similarity results are very sensitive to the selection of strain/strain-rate and often leads to failed predictions. In addition, for the material elastic and temperature effects, the proposed method is also discussed to be valid.

2016 ◽  
Vol 1812 ◽  
pp. 41-46
Author(s):  
Elvira García-Mora ◽  
Ignacio Mejía ◽  
Francisco Reyes-Calderón ◽  
José M. Cabrera

ABSTRACTWhen high strength and high ductility are required, the Twinning Induced Plasticity steels are an excellent choice. Their mechanical advantages are perfectly known in the automotive industry. Then, they are currently deeply studied. During the deformation at high temperature, TWIP steel experiences dynamic recrystallization. This mechanism results from dislocation interactions, and it depends of temperature, stress, strain, and strain rate. Experimental data give the maximum stress reached by the material, but the critical stress which determinates the DRX onset must be calculated from the strain hardening rate. Both stress and strain change simultaneously, and this variation gives the analytic data to determine σc, which is located at the inflection point of θ-σ plot. The main purpose of this paper was to study how the chemical composition and the experimental parameters (temperature and strain rate) affect the DRX, by the calculation and analysis of the σc values. Hot compression tests were applied to a pair of TWIP steels to compare the DRX onset and its relationship with the vanadium addition. The experimental variables were temperature and strain rate. The true stress–true strain plots were used to calculate σc by cutting data up to a previous point before the σp value, then, a polynomial fit and derivation were applied. The Zener-Hollomon parameter (Z) versus the stresses (peak and critical) plots show how the micro-alloying element vanadium improves the strain hardening in the analyzed TWIP steels.


2005 ◽  
Vol 20 (6) ◽  
pp. 1447-1455 ◽  
Author(s):  
H.G. Jeong ◽  
W.J. Kim

The superplastic behavior of the Zr65Al10Ni10Cu15 glass metallic alloy produced by the powder metallurgy method was examined in the supercooled liquid region. A tensile elongation as large as 750% was obtained at 6.3 × 10−3 s−1 at 697 K. Large strain hardening took place during the course of deformation and systematic trend was observed in the hardening behavior. Plots of stress versus strain and strain rate versus stress at 697 K showed that Newtonian viscous flow governed the plastic flow until the onset of strain hardening. Microstructure and differential scanning calorimetry analyses as well as flow stress versus testing time curves provided consistent evidence that the strain hardening was induced by crystallization. Crystallization was enhanced in the gauge region (deformed region) as compared to the grip region (undeformed region). Crystallization is expected to decrease tensile ductility by decreasing the strain-rate-sensitivity value and increasing the degree of brittleness. Hardening by crystallization, however, can contribute to neck stability if crystallization is enhanced in the neck region. The strain hardening and plastic stability parameters were measured as a function of strain for different strain rates at 696 K. The strain hardening parameter remained highly positive until failure. Because of this, the neck stability parameter (I) could be I < 0 in the entire hardening region. The contribution of hardening by crystallization to neck stability was found to be much more significant than that by grain growth in the superplastic metallic alloys. Reducing the specimen heating-and-holding time was suggested to promote superplasticity deformation without delaying initiation of crystallization. The largest tensile strain in the hardening region where crystallization may be obtained at the strain rates and temperatures where crystallization rate is controlled to be the lowest while maintaining I ≤ 0 throughout deformation.


1967 ◽  
Vol 2 (4) ◽  
pp. 257-264
Author(s):  
E A Davis

The distribution of the stress, strain, and strain rate in a long rod, one end of which has been given a fixed velocity, is analysed. Computer programmes have been written for three different classes of materials: purely rate-sensitive materials, purely strain-hardening materials, and materials exhibiting both strain hardening and speed effect. Where possible the results have been checked against known solutions.


Author(s):  
Shuai Wang ◽  
Fei Xu ◽  
Xiaoyu Zhang ◽  
Zhen Dai

A framework of similarity laws, termed oriented-density-length-velocity (ODLV) framework, is suggested for the geometric distorted structures subjected to impact loading. The distinct feature of this framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for physical quantity are explicitly expressed by the characteristic lengths of three spatial directions, which overcome the inherent defects that traditional scalar dimensional analysis could not express the effects of structural geometric characteristics and spatial directions for similarity. The non-scalabilities of geometrical distortion as well as other distortions such as different materials and gravity could be compensated by the reasonable correction for the impact velocity, the geometrical thickness and the density, when the proposed dimensionless number of equivalent stress is used between scaled model and prototype. Three analytical models of beam, plate and shell subjected to impact mass or impulsive velocity are verified by equation analysis. And a numerical model of circular plate subjected to dynamic pressure pulse is verified in more detail, form the view of point of space deformation, deformation history and the components of displacement, strain and stress. The results show that the proposed dimensionless numbers have attractively perfect ability to express the dimensionless response equations of displacement, angle, time, strain and strain rate. When the proposed dimensionless numbers are used to regularize impact models, the structural responses of the geometrically distorted scaled models can behave the completely identical behaviors with those of the prototype on space and time &mdash;not only for the direction-independent equivalent stress, strain and strain rate but also for the direction-dependent displacement, stress and strain components.


Author(s):  
M. F. Stevens ◽  
P. S. Follansbee

The strain rate sensitivity of a variety of materials is known to increase rapidly at strain rates exceeding ∼103 sec-1. This transition has most often in the past been attributed to a transition from thermally activated guide to viscous drag control. An important condition for imposition of dislocation drag effects is that the applied stress, σ, must be on the order of or greater than the threshold stress, which is the flow stress at OK. From Fig. 1, it can be seen for OFE Cu that the ratio of the applied stress to threshold stress remains constant even at strain rates as high as 104 sec-1 suggesting that there is not a mechanism transition but that the intrinsic strength is increasing, since the threshold strength is a mechanical measure of intrinsic strength. These measurements were made at constant strain levels of 0.2, wnich is not a guarantee of constant microstructure. The increase in threshold stress at higher strain rates is a strong indication that the microstructural evolution is a function of strain rate and that the dependence becomes stronger at high strain rates.


Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2021
Author(s):  
Oleksandr Lypchanskyi ◽  
Tomasz Śleboda ◽  
Aneta Łukaszek-Sołek ◽  
Krystian Zyguła ◽  
Marek Wojtaszek

The flow behavior of metastable β titanium alloy was investigated basing on isothermal hot compression tests performed on Gleeble 3800 thermomechanical simulator at near and above β transus temperatures. The flow stress curves were obtained for deformation temperature range of 800–1100 °C and strain rate range of 0.01–100 s−1. The strain compensated constitutive model was developed using the Arrhenius-type equation. The high correlation coefficient (R) as well as low average absolute relative error (AARE) between the experimental and the calculated data confirmed a high accuracy of the developed model. The dynamic material modeling in combination with the Prasad stability criterion made it possible to generate processing maps for the investigated processing temperature, strain and strain rate ranges. The high material flow stability under investigated deformation conditions was revealed. The microstructural analysis provided additional information regarding the flow behavior and predominant deformation mechanism. It was found that dynamic recovery (DRV) was the main mechanism operating during the deformation of the investigated β titanium alloy.


Nanomaterials ◽  
2019 ◽  
Vol 9 (8) ◽  
pp. 1088 ◽  
Author(s):  
Yang Kang ◽  
Dunhong Zhou ◽  
Qiang Wu ◽  
Fuyan Duan ◽  
Rufang Yao ◽  
...  

The physical properties—including density, glass transition temperature (Tg), and tensile properties—of polybutadiene (PB), polystyrene (PS) and poly (styrene-butadiene-styrene: SBS) block copolymer were predicted by using atomistic molecular dynamics (MD) simulation. At 100 K, for PB and SBS under uniaxial tension with strain rate ε ˙ = 1010 s−1 and 109 s−1, their stress–strain curves had four features, i.e., elastic, yield, softening, and strain hardening. At 300 K, the tensile curves of the three polymers with strain rates between 108 s−1 and 1010 s−1 exhibited strain hardening following elastic regime. The values of Young’s moduli of the copolymers were independent of strain rate. The plastic modulus of PS was independent of strain rate, but the Young’s moduli of PB and SBS depended on strain rate under the same conditions. After extrapolating the Young’s moduli of PB and SBS at strain rates of 0.01–1 s−1 by the linearized Eyring-like model, the predicted results by MD simulations were in accordance well with experimental results, which demonstrate that MD results are feasible for design of new materials.


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