Constitutive Modeling of a Thermoplastic Olefin Over a Broad Range of Strain Rates

2006 ◽  
Vol 128 (4) ◽  
pp. 551-558 ◽  
Author(s):  
Yan Wang ◽  
Ellen M. Arruda

A microstructually motivated, three-dimensional, large deformation, strain rate dependent constitutive model has been developed for a semi-crystalline, blended, thermoplastic olefin (TPO) (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). Various experiments have been conducted to characterize the TPO and to verify the modeling approach (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). The model includes a quantitative rate-dependent Young’s modulus, a nonlinear viscoelastic response between initial linear elastic response and yield due to inherent microstructural irregularity, rate and temperature dependent yield with two distinctive yield mechanisms for low and high strain rates, temperature-dependent strain hardening, plastic deformation of crystalline regions, and adiabatic heating. It has been shown to accurately capture the observed TPO stress-strain behavior including the rate-dependent initial linear elastic response; temperature, strain rate, and deformation state-dependent yield; temperature and deformation state-dependent strain hardening; and pronounced thermal softening effects at high (impact) strain rates. The model has also been examined for its ability to predict the response in plane strain compression based on material parameters chosen to capture the uniaxial compression response. The model is predictive of the initial strain rate dependent stiffness, yield, and strain hardening responses in plane strain. Such predictive capability demonstrates the versatility with which this model captures the three-dimensional anisotropic nature of TPO stress-strain behavior.

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.


Author(s):  
Christopher B. Finfrock ◽  
Melissa M. Thrun ◽  
Diptak Bhattacharya ◽  
Trevor J. Ballard ◽  
Amy J. Clarke ◽  
...  

2007 ◽  
Vol 558-559 ◽  
pp. 441-448 ◽  
Author(s):  
Jong K. Lee

During hot working, deformation of metals such as copper or austenitic steels involves features of both diffusional flow and dislocation motion. As such, the true stress-true strain relationship depends on the strain rate. At low strain rates (or high temperatures), the stress-strain curve displays an oscillatory behavior with multiple peaks. As the strain rate increases (or as the temperature is reduced), the number of peaks on the stress-strain curve decreases, and at high strain rates, the stress rises to a single peak before settling at a steady-state value. It is understood that dynamic recovery is responsible for the stress-strain behavior with zero or a single peak, whereas dynamic recrystallization causes the oscillatory nature. In the past, most predictive models are based on either modified Johnson-Mehl-Avrami kinetic equations or probabilistic approaches. In this work, a delay differential equation is utilized for modeling such a stress-strain behavior. The approach takes into account for a delay time due to diffusion, which is expressed as the critical strain for nucleation for recrystallization. The solution shows that the oscillatory nature depends on the ratio of the critical strain for nucleation to the critical strain for completion for recrystallization. As the strain ratio increases, the stress-strain curve changes from a monotonic rise to a single peak, then to a multiple peak behavior. The model also predicts transient flow curves resulting from strain rate changes.


2020 ◽  
Author(s):  
Chuang Liu ◽  
Dongzhi Sun ◽  
Xianfeng Zhang ◽  
Florence Andrieux ◽  
Tobias Gerster

Abstract Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry. To study the mechanical behavior of a typical ductile cast iron (GJS-450) with nodular graphite, uni-axial quasi-static and dynamic tensile tests at strain rates of 10− 4, 1, 10, 100, and 250 s− 1 were carried out. In order to investigate the effects of stress state, specimens with various geometries were used in the experiments. Stress–strain curves and fracture strains of the GJS-450 alloy in the strain-rate range of 10− 4 to 250 s− 1 were obtained. A strain rate-dependent plastic flow law based on the Voce model is proposed to describe the mechanical behavior in the corresponding strain-rate range. The deformation behavior at various strain rates is observed and analyzed through simulations with the proposed strain rate-dependent constitutive model. The available damage model from Bai and Wierzbicki is extended to take the strain rate into account and calibrated based on the analysis of local fracture strains. The validity of the proposed constitutive model including the damage model was verified by the corresponding experimental results. The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys. The predictions with the proposed constitutive model and damage models at various strain rates agree well with the experimental results, which illustrates that the rate-dependent flow rule and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.


Metals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 344 ◽  
Author(s):  
Simon Sevsek ◽  
Christian Haase ◽  
Wolfgang Bleck

The strain-rate-dependent deformation behavior of an intercritically annealed X6MnAl12-3 medium-manganese steel was analyzed with respect to the mechanical properties, activation of deformation-induced martensitic phase transformation, and strain localization behavior. Intercritical annealing at 675 °C for 2 h led to an ultrafine-grained multi-phase microstructure with 45% of mostly equiaxed, recrystallized austenite and 55% ferrite or recovered, lamellar martensite. In-situ digital image correlation methods during tensile tests revealed strain localization behavior during the discontinuous elastic-plastic transition, which was due to the localization of strain in the softer austenite in the early stages of plastic deformation. The dependence of the macroscopic mechanical properties on the strain rate is due to the strain-rate sensitivity of the microscopic deformation behavior. On the one hand, the deformation-induced phase transformation of austenite to martensite showed a clear strain-rate dependency and was partially suppressed at very low and very high strain rates. On the other hand, the strain-rate-dependent relative strength of ferrite and martensite compared to austenite influenced the strain partitioning during plastic deformation, and subsequently, the work-hardening rate. As a result, the tested X6MnAl12-3 medium-manganese steel showed a negative strain-rate sensitivity at very low to medium strain rates and a positive strain-rate sensitivity at medium to high strain rates.


2019 ◽  
Vol 89 (18) ◽  
pp. 3825-3838
Author(s):  
Ahmad Abuobaid ◽  
Raja Ganesh ◽  
John W Gillespie

A dynamic loop test method for measuring strain rate-dependent fiber properties was developed. During dynamic loop testing, the fiber ends are accelerated at constant levels of 20.8, 50 and 343 m/s2. The test method is used to study Kevlar® KM2-600, which fails in axial compression due to kink band formation. The compressive failure strain and strain rate at the onset of kink band formation is calculated from the critical loop diameter ( D C), which is monitored throughout the test using a high-speed camera. The results showed that compressive failure strain increases with strain rates from quasi-static to a maximum strain rate of 116 s−1 by a factor of ∼3. Kink angles (φ) and kink band spacing ( D S) were 60 ° ± 2 ° and 16 ± 3 μm, respectively, over the strain rates tested. Rate-dependent mechanisms of compressive failure by kink band formation were discussed.


2019 ◽  
Vol 794 ◽  
pp. 135-141
Author(s):  
Bin Zhang ◽  
Yang Wang

The mechanical responses of Ti-5Al-2.5Sn alloy at low temperatures were investigated under quasi-static and dynamic tensile loads using MTS system and SHTB system, respectively. Tensile stress-strain curves were obtained over the temperature range of 153 to 298K and the rate range of 0.001 to 1050 s-1. Experimental results indicate that the tensile behavior of Ti-5Al-2.5Sn alloy is dependent on strain rate and temperature. Yield stress and flow stress increase with increasing strain rate and decrease with increasing temperature. Results also indicate that strain hardening rate of Ti-5Al-2.5Sn alloy is lower at high strain rate, while strain hardening rate varies little with testing temperature. The Khan-Huang-Liang constitutive model was chosen to characterize the tensile responses of Ti-5Al-2.5Sn alloy at low temperatures and different strain rates. The model results coincide well with the experimental results within the tested temperature and rate ranges.


1980 ◽  
Vol 15 (4) ◽  
pp. 201-207 ◽  
Author(s):  
M S J Hashmi

Experimental results on a mild steel are reported from ballistics tests which gave rise to strain rates of up to 105 s−1. A finite-difference numerical technique which incorporates material inertia, elastic-strain hardening and strain-rate sensitivity is used to establish the strain-rate sensitivity constants p and D in the equation, σ4 = σ1 (1+(∊/D)1/ p). The rate sensitivity established in this study is compared with those reported by other researchers.


2014 ◽  
Vol 566 ◽  
pp. 80-85
Author(s):  
Kenji Nakai ◽  
Takashi Yokoyama

The present paper is concerned with constitutive modeling of the compressive stress-strain behavior of selected polymers at strain rates from 10-3 to 103/s using a modified Ramberg-Osgood equation. High strain-rate compressive stress-strain curves up to strains of nearly 0.08 for four different commercially available extruded polymers were determined on the standard split Hopkinson pressure bar (SHPB). The low and intermediate strain-rate compressive stress-strain relations were measured in an Instron testing machine. Six parameters in the modified Ramberg-Osgood equation were determined by fitting to the experimental stress-strain data using a least-squares fit. It was shown that the monotonic compressive stress-strain behavior over a wide range of strain rates can successfully be described by the modified Ramberg-Osgood constitutive model. The limitations of the model were discussed.


1973 ◽  
Vol 13 (04) ◽  
pp. 211-220 ◽  
Author(s):  
T.K. Perkins ◽  
R.A. Ruedrich

Abstract Discoveries of oil in Arctic regions have led to several engineering problems that are relatively new to the petroleum industry. An understanding of some of the new problems associated with construction of surface facilities as well as with the drilling and completion of wells requires an understanding of the mechanical properties of permafrost. permafrost. Synthetic permafrost samples have been prepared from quartz sand as well as from natural soils taken from Prudhoe Bay permafrost cores recovered from depths as great as 1,753 It. All samples have been recompacted and frozen under a condition of zero confining stress. Samples prepared in this way should exhibit behavior similar to that of shallow permafrost. Samples have been tested in uniaxial permafrost. Samples have been tested in uniaxial compression at constant strain rates as well as with constant axial stress. At constant temperature and low strain rates, the log of the maximum shear strength will plot as a straight line vs the log of the strain rate. For sand-ice samples at high strain rate, another mode of failure was evident that led to a maximum shear strength independent of strain rate. Under triaxial conditions, the maximum shear strength of sand-ice samples was generally increased with increasing stress level. In uniaxial tension, the tensile strength of sand-ice samples was found to be a function of temperature and strain rate. Elastic response of these samples was obscured by the more dominant flow behavior at low strain rates. Only at clearly high strain rates was an elastic response clearly discernible. Young's modulus measured after 10 to 15 percent plastic strain increases with increasing stress level. Introduction Within the last few years significant oil discoveries have been made in Arctic regions. There is much speculation that additional oil will be found in regions that are characterized by quite low ambient and soil temperatures. The drilling of wells and production of oil under these environmental conditions poses new problems not traditionally faced by the petroleum industry, but which presumably will be of increasing concern within the presumably will be of increasing concern within the next few years. One new engineering challenge is that of dealing with permafrost, soil which has been continuously frozen for a number of years. Already at Prudhoe Bay a number of wells have been drilled through about 2,000 ft of permafrost. As an example of permafrost influence, measurements have shown that, when thawed permafrost around a well refreezes, significant pressures can be generated. In order to understand this phenomenon, it will be necessary to understand the mechanical behavior of permafrost. In addition, surface facilities have been permafrost. In addition, surface facilities have been constructed where there is a thin, active region (which thaws during summer months) underlain by permafrost. An understanding of permafrost permafrost. An understanding of permafrost mechanical behavior will aid in the design of foundations for surface facilities. There are a number of variables that can influence the mechanical behavior of frozen soils such as minerology, percent of ice saturation, presence of excess ice, salt content, etc. In this paper we will describe a laboratory study of relatively fine-grained granular materials with pore spaces saturated with ice. The results presented here may not be applicable to frozen clays or gravels, where pore spaces are undersaturated or where a large amount of excess ice is present. Since permafrost is composed of ice and soil, its behavior will naturally reflect that of its constituents. The rate of yield or flow of ice is known to be a function of temperature, shear stress and strain, but is independent of hydrostatic pressure level. Soil, on the other hand, exhibits pressure level. Soil, on the other hand, exhibits yield behavior that is independent of temperature over the small range of permafrost temperatures of interest. For sandy soil, yield behavior is relatively independent of strain rate, but is significantly influenced by strain and stress level. Under stress, a dominant characteristic of shallow permafrost is that of yield or flow. Its rate of flow will be a function of all the variables mentioned above. Over-all deformation results from a combination of elastic and flow behavior. SPEJ P. 211


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