Strength of Metals and Alloys at High Strains and Strain Rates

The introduction of inertia terms into a theoretical model of thin ring expansion shows that classical plastic instability concepts, defined in terms of the local strain in the necking region, no longer apply. By introducing the role of void growth in triggering local necking, through a recently proposed constitutive equation for porous plastic materials, it is possible to overcome this difficulty. A criterion based on a critical void volume fraction provides the alternative means to predict failure. This theory was applied to a thin ring configuration, and the results were found to compare favorably with experimental values obtained from statically and dynamically loaded rings. The experimental techniques developed to handle the thin ring configuration are also described. IntroductionDuctile failure as a phenomenon associated with plastic instability dates back to the time of Considere [1] who identified the point of instability as the onset of localized necking brought about when the increment of strain hardening became equal to the geometric softening, at the point of maximum load in a simple tension test. Marciniak and Kuczynski [2] considered this phenomenon in metal sheets under biaxial tension, and developed a mathematical model (M-K model) to construct forming limit diagrams. This model is based on an initial geometric imperfection, which is a localized thickness reduction in the sheet lying perpendicular to the major principal strain direction. By this method they predicted that the strain in the uniform region reaches a limiting value at which point the local strain in the defective region becomes unstable. In recent studies by Hutchinson and Neale [3] and Ghosh [4] the analysis was extended to include the effect of strain rate and different viscoplastic constitutive laws on localized necking. The results of this analysis, in its application to the case of uniaxial tension under quasi-static loading, predicted that the strain at necking increases with an increase in the strain-rate sensitivity and the strain-hardening parameter. These results were verified experimentally for different materials by Ghosh [4]. This analysis also predicted, depending on the constitutive equation, either no effect on or minor reduction of uniform strain at necking due to an increase in strain rate. These theoretical results were in agreement with the experiments of Sagat and Taplin [5] for superplastic materials under quasi-static loading conditions.In the high strain-rate loading regime, where the quasistatic loading assumption no longer applies, considerable evidence exists, Wilson [6], that an increase in strain rate can

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“…30 dcjy (15) and the elastic constants of the matrix are given in terms of Young's modulus E, arid Poisson's ration v, by…”

Section: Compressible Materialsmentioning

confidence: 99%

Inertia Effects on the Ductile Failure of Thin Rings

Rajendran

Fyfe

1982

Journal of Applied Mechanics

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“…Frantz and Du y [49] used this apparatus in the incremental strain rate experiment. e strain rate of the aluminum specimen increased from 5 × 10 −5 s −1 to 850 s −1 in 10 ms. Campbell et al [75] used the same apparatus to study the in uence of the strain rate and strain rate history on the strength of materials. Similar to the explosive loading TSHB, the prestored energy loading TSHB have also been developed for the combined loading of quasistatic and high strain rate torsions [57], as shown in Figure 21.…”

Section: Combined Loading Tests For Quasistatic and Highmentioning

confidence: 99%

A Review of the Torsional Split Hopkinson Bar

Chen

Fang

et al. 2018

Advances in Civil Engineering

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Mechanical behavior of materials at medium and high strain rates (101∼104 s−1) is the foundation of developing mechanical theories, building material models, and promoting engineering design and construction. The torsional split Hopkinson bar (TSHB) is an effective experimental technique for measuring the pure shear mechanical properties of materials at high strain rates. In this study, the state-of-the-art in TSHB experimental technique is presented. Five typical types of TSHB loading mechanisms, i.e., prestored energy loading, explosive loading, direct impact loading, flywheel loading, and electromagnetic loading, were systematically reviewed. The TSHB fundamentals were outlined, which include elementary components, basic assumptions, working principles, the pulse shaping technique, specimen design, and the single-pulse loading technique. In addition, the combined loading and high/low temperature experimental techniques, which were developed based on TSHB, were also discussed in detail. Nearly all necessary elements for conducting a TSHB experiment and analyzing the experimental data were provided. Some research directions should be further pursued, such as extending the range of applicable materials and developing the combined loading techniques.

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“…To describe the deformation behavior of crystalline metals at different strain rates and temperatures, many constitutive models had been established in the past years. Simple uniaxial stress–strain model and one-dimensional stress wave propagation model had been proposed initially to describe the temperature and strain rate effects on the flow stress 14 , 15 . Then, some phenomenological models had been developed sequentially.…”

Section: Introductionmentioning

confidence: 99%

A strain rate dependent thermo-elasto-plastic constitutive model for crystalline metallic materials

Chen

Wang

2021

Sci Rep

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The strain rate and temperature effects on the deformation behavior of crystalline metal materials have always been a research hotspot. In this paper, a strain rate dependent thermo-elasto-plastic constitutive model was established to investigate the deformation behavior of crystalline metal materials. Firstly, the deformation gradient was re-decomposed into three parts: thermal part, elastic part and plastic part. Then, the thermal strain was introduced into the total strain and the thermo-elastic constitutive equation was established. For the plastic behavior, a new relation between stress and plastic strain was proposed to describe the strain rate and temperature effects on the flow stress and work-hardening. The stress–strain curves were calculated over wide ranges of strain rates (10–6–6000 s−1) and temperatures (233–730 K) for three kinds of crystalline metal materials with different crystal structure: oxygen free high conductivity copper for face centered cubic metals, Tantalum for body centered cubic metals and Ti–6Al–4V alloy for two phase crystal metals. The comparisons between the calculation and experimental results reveal that the present model describes the deformation behavior of crystalline metal materials well. Also, it is concise and efficient for the practical application.

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Strength of Metals and Alloys at High Strains and Strain Rates

Cited by 21 publications

References 19 publications

Inertia Effects on the Ductile Failure of Thin Rings

Inertia Effects on the Ductile Failure of Thin Rings

A Review of the Torsional Split Hopkinson Bar

A strain rate dependent thermo-elasto-plastic constitutive model for crystalline metallic materials

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