A strain rate dependent constitutive model for clays at residual strength

1998 ◽  
Vol 35 (2) ◽  
pp. 364-373 ◽  
Author(s):  
AMP Wedage ◽  
N R Morgenstern ◽  
D H Chan
Keyword(s):  
Plastic Deformation ◽  
Strain Rate ◽  
Residual Strength ◽  
Plasticity Theory ◽  
Constitutive Relationship ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Rate Dependent ◽  
Dependent Part ◽  
Rate Effects

Plasticity theory is extended to incorporate strain rate effects on the residual shear strength of clays. The clay is assumed to behave elastically before yielding and then in a perfectly plastic manner with no volume change during yielding. The Mohr-Coulomb failure criterion is used in the rate-dependent model in which the strain rate affects the mobilized effective friction angle of the material. During initial yielding and subsequent plastic deformation, the stress and strain states at a point will satisfy the rate-dependent yield function (loading function). When the effective plastic strain rate decreases to a threshold strain value, the loading surface moves, or collapses, to the static yield surface. A constant volume flow rule is used to calculate plastic deformation. The computed stress-strain relationship is formulated in two parts, namely a rate-independent part and a rate-dependent part. The rate-independent part is the same as that used in classical elastoplastic formulations, whereas the rate-dependent part is dependent on the current strain rate of the material. The use of the model is illustrated using a numerical example simulating a two-dimensional plane strain test.Key words: constitutive relationship, finite element, plasticity theory, pre-sheared clay, rate effects, residual strength.

scholarly journals How to Realize Volume Conservation During Finite Plastic Deformation

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Heling Wang ◽  
Dong-Jie Jiang ◽  
Li-Yuan Zhang ◽  
Bin Liu
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Plastic Strain Rate ◽  
Strain Rate Tensor ◽  
Cauchy Stress ◽  
Volume Conservation ◽  
Tangential Stiffness ◽  
Manufacture Process ◽  
Universal Approach

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e., the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples. The potential application of the proposed theories is a better simulation of manufacture process such as metal forming.

Simulation of time-dependent movements in Syncrude tailings dyke foundation

1998 ◽  
Vol 35 (2) ◽  
pp. 284-298 ◽  
Author(s):  
AMP Wedage ◽  
N R Morgenstern ◽  
D H Chan
Keyword(s):  
Residual Strength ◽  
Time Dependent ◽  
Deformation Analysis ◽  
Foundation Soil ◽  
Clay Shale ◽  
Soil Plasticity ◽  
Rate Dependent ◽  
Rate Effects ◽  
Clearwater Formation ◽  
Using Data

Foundation movements at the Syncrude tailings dyke continued over several years in response to the construction of the dyke. Major movements have been observed in a relatively narrow layer of previously sheared clay-shale material of the Clearwater Formation. The residual strength of this highly plastic clay increases with the rate of shear. By reviewing the existing literature on the rate effects on residual strength and using data from new experiments on Clearwater Clay Shale, a general correlation between soil plasticity and rate effects is found. This rate dependence of the residual strength of Clearwater clay shale has been incorporated into a deformation analysis, which made it possible to compute time-dependent movements of the foundation soil to a satisfactory level. By using a rate-dependent plasticity model, a prediction of anticipated foundation velocities and how they decrease with time may be achieved.Key words: finite element, rate effects, residual strength, Syncrude tailings dyke, time-dependent movements.

scholarly journals An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems

2018 ◽  
Vol 45 (2) ◽  
pp. 177-188
Author(s):  
Adebowale Borokinni ◽  
Odunayo Fadodun ◽  
Adegbola Akinola
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Plane Strain ◽  
Strain Gradient ◽  
Dissipative Process ◽  
Strain Gradient Plasticity ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Gradient Plasticity ◽  
Plane Strain Problem

This article considers a plane strain gradient plasticity theory of the Gurtin?Anand model [M. Gurtin, L. Anand, A theory of strain gradient plasticity for isotropic, plastically irrotational materials Part I: Small deformations, J. Mech. Phys. Solids 53 (2005), 1624?1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin?Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.

scholarly journals Review of Strain Rate Effects of Fiber-Reinforced Polymer Composites

Polymers ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2839
Author(s):  
Lulu Ma ◽  
Feng Liu ◽  
Dongyu Liu ◽  
Yaolu Liu
Keyword(s):  
Strain Rate ◽  
Numerical Models ◽  
Fiber Reinforced Polymer ◽  
Fiber Reinforced ◽  
Strain Rate Effects ◽  
Frp Composites ◽  
Rate Dependent ◽  
Reinforced Polymer ◽  
Fiber Reinforced Polymer Composites ◽  
Rate Effects

The application of fiber-reinforced polymer (FRP) composites is gaining increasing popularity in impact-resistant devices, automotives, biomedical devices and aircraft structures due to their high strength-to-weight ratios and their potential for impact energy absorption. Impact-induced high loading rates can result in significant changes of mechanical properties (e.g., elastic modulus and strength) before strain softening occurs and failure characteristics inside the strain localization zone (e.g., failure mechanisms and fracture energy) for fiber-reinforced polymer composites. In general, these phenomena are called the strain rate effects. The underlying mechanisms of the observed rate-dependent deformation and failure of composites take place among multiple length and time scales. The contributing mechanisms can be roughly classified as: the viscosity of composite constituents (polymer, fiber and interfaces), the rate-dependency of the fracture mechanisms, the inertia effects, the thermomechanical dissipation and the characteristic fracture time. Numerical models, including the viscosity type of constitutive models, rate-dependent cohesive zone models, enriched equation of motion and thermomechanical numerical models, are useful for a better understanding of these contributing factors of strain rate effects of FRP composites.

Strain Rate Sensitivity of Commercial Aluminum Alloys

2019 ◽  
Author(s):  
R.C. Picu
Keyword(s):  
Plastic Deformation ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Solid Solutions ◽  
Elevated Temperatures ◽  
Rate Sensitivity ◽  
Solute Diffusion ◽  
Rate Dependent ◽  
Ultrafine Grained ◽  
Using Data

This article presents a review of the strain rate-dependent mechanical behavior of aluminum and its commercial alloys. The importance of strain rate sensitivity (SRS) stems from its relation with ductility and formability. Plastic deformation is stable and localization less likely in alloys with higher SRS. After discussing the basic formulation used to interpret experimental data, the methods used to measure the SRS parameter are presented. This is followed by a brief review of the main mechanisms that render the flow stress sensitive to the deformation rate, including mechanisms leading to positive and negative SRS. The generic dependence of the SRS parameter on the strain, temperature, and strain rate are further presented using data for pure Al. The effect of alloying is analyzed in the context of solid solutions and precipitated commercial alloys. Results on solid solutions are discussed separately at low and elevated temperatures in order to evidence the role of solute diffusion on SRS. This article ends with a brief discussion of the grain size dependence of SRS, with emphasis on recent efforts to produce nanocrystalline and ultrafine-grained materials by severe plastic deformation.

scholarly journals Strain rate dependence of plastic flow in Ce-based bulk metallic glass during nanoindentation

2007 ◽  
Vol 22 (2) ◽  
pp. 258-263 ◽  
Author(s):  
B.C. Wei ◽  
L.C. Zhang ◽  
T.H. Zhang ◽  
D.M. Xing ◽  
J. Das ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Metallic Glass ◽  
Strain Rate ◽  
Bulk Metallic Glass ◽  
Loading Rate ◽  
Shear Banding ◽  
Rate Dependence ◽  
Strain Rate Dependence ◽  
Serrated Flow ◽  
Rate Dependent

The strain rate dependence of plastic deformation of Ce60Al15Cu10Ni15 bulk metallic glass was studied by nanoindentation. Even though the ratio of room temperature to the glass transition temperature was very high (0.72) for this alloy, the plastic deformation was dominated by shear banding under nanoindentation. The alloy exhibited a critical loading rate dependent serrated flow feature. That is, with increasing loading rate, the alloy exhibited a transition from less prominent serrated flow to pronounced serrated flow during continuous loading but from serrated to smoother flow during stepped loading.

scholarly journals Strain-rate-dependent properties of short carbon fiber-reinforced acrylonitrile-butadiene-styrene using material extrusion additive manufacturing

2020 ◽  
Vol 26 (10) ◽  
pp. 1701-1712
Author(s):  
Wilco M.H. Verbeeten ◽  
Miriam Lorenzo-Bañuelos ◽  
Rubén Saiz-Ortiz ◽  
Rodrigo González
Keyword(s):  
Carbon Fiber ◽  
Strain Rate ◽  
Acrylonitrile Butadiene Styrene ◽  
Rate Dependence ◽  
Strain Rate Dependence ◽  
Flow Rule ◽  
Content Type ◽  
Short Carbon Fiber ◽  
Rate Dependent ◽  
Short Carbon

Purpose The purpose of the present paper is to quantify and analyze the strain-rate dependence of the yield stress for both unfilled acrylonitrile-butadiene-styrene (ABS) and short carbon fiber-reinforced ABS (CF-ABS) materials, fabricated via material extrusion additive manufacturing (ME-AM). Two distinct and opposite infill orientation angles were used to attain anisotropy effects. Design/methodology/approach Tensile test samples were printed with two different infill orientation angles. Uniaxial tensile tests were performed at five different constant linear strain rates. Apparent densities were measured to compensate for the voided structure. Scanning electron microscope fractography images were analyzed. An Eyring-type flow rule was evaluated for predicting the strain-rate-dependent yield stress. Findings Anisotropy was detected not only for the yield stresses but also for its strain-rate dependence. The short carbon fiber-filled material exhibited higher anisotropy than neat ABS material using the same ME-AM processing parameters. It seems that fiber and molecular orientation influence the strain-rate dependence. The Eyring-type flow rule can adequately describe the yield kinetics of ME-AM components, showing thermorheologically simple behavior. Originality/value A polymer’s viscoelastic behavior is paramount to be able to predict a component’s ultimate failure behavior. The results in this manuscript are important initial findings that can help to further develop predictive numerical tools for ME-AM technology. This is especially relevant because of the inherent anisotropy that ME-AM polymer components show. Furthermore, short carbon fiber-filled ABS enhanced anisotropy effects during ME-AM, which have not been measured previously.

Strain-Rate Effects in the Propagation of Torsional Plastic Waves

1966 ◽  
Vol 33 (4) ◽  
pp. 917-923 ◽  
Author(s):  
W. E. Baker ◽  
C. H. Yew
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Cross Sections ◽  
Pure Copper ◽  
High Rate ◽  
Strain Rate Effects ◽  
Rate Dependent ◽  
Dependent Theory ◽  
Lower Strain ◽  
Rate Effects

A new method was developed for determining the dynamic stress-strain relationships of materials subjected to high rate of torsional loading. In addition, an investigation of propagation of torsional plastic waves in a long tube was conducted. Commercially pure copper was used throughout both investigations. In the material property studies, shear strains up to 20 percent and shear strain rates to 2100/sec were obtained. The results indicated that copper exhibits significantly lower strain-rate effects than those previously obtained by the longitudinal loading method. In the studies of plastic wave propagation, shear strain-time records at several cross sections along the tube were compared with computed results obtained from the strain-rate-independent and strain-rate-dependent theories. It is concluded that the computed results based on the strain-rate-dependent theory give better agreement with the experiments.

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