Strain localization due to structural softening during pressure sensitive rate independent yielding

2013 ◽  
Vol 184 (4-5) ◽  
pp. 357-371 ◽  
Author(s):  
Laetitia Le Pourhiet
Keyword(s):  
Shear Band ◽  
Strain Softening ◽  
Shear Bands ◽  
Limit Load ◽  
Friction Angle ◽  
Stress Axis ◽  
Flow Rule ◽  
Finite Limit ◽  
Confining Stress ◽  
Pressure Sensitive

Abstract After giving a complete analytical solution for the strain softening model associated to Mohr-Coulomb non associated elasto-plastic flow rule (MC-model), the paper demonstrates that this rheology possesses a finite limit load which allows solving for strength drop as a boundary value problem. The MC-model produces a non-dimensional strength drop, which depends on three parameters: the orientation of the shear band versus the least principal stress axis outside the band α0, the peak friction angle φ and the dilatation angle Ψ. The maximum reduction of strength obtained with that strain-softening model is on the order of the confining stress p0. For this weakest regime, the effective friction of the shear band drops from μini = 0.85 at peak to μss = 0.64 at the end of the softening phase. In this model, which considers thick shear bands, the weakest regime is not obtained for an orientation corresponding to the exact Coulomb orientation. Instead, the orientation of the weakest shear zone systematically deviates from the coulomb orientation by an angle, which rises with its internal friction angle. The characteristic shear strain needed to achieve steady state is quantified semi analytically and in the range of parameters valid for Earth, this strain is found to be of the order of 7–8%. These numbers are typical of what is observed in the laboratory, which give us confidence on that MC-model is a good and probably the simplest model to localize strain in numerical codes aimed at modeling the brittle part of the Earth.

On the Crucial Role of Imperfections in Quasi-static Viscoplastic Solutions

1991 ◽  
Vol 58 (3) ◽  
pp. 658-665 ◽  
Author(s):  
T. Belytschko ◽  
B. Moran ◽  
M. Kulkarni
Keyword(s):  
Shear Band ◽  
Strain Softening ◽  
Shear Bands ◽  
Step Function ◽  
Viscoplastic Material ◽  
One Dimensional ◽  
Initial Imperfections ◽  
Dimensional Boundary ◽  
The Stability

The stability and structure of shear bands and how they relate to initial imperfections is studied within the framework of a one-dimensional boundary value problem. It is shown that in strain-softening viscoplasticity the structure of the band depends on the structure of the imperfection. A Fourier analysis shows that the width of the shear band depends directly on the width of the imperfection, suggesting that the imperfection scales the response of the viscoplastic material. For continuously differentiable imperfections, the shear band is continuously differentiable, whereas when the imperfection is C° at the maximum, the shear band is C°, and cusp-shaped. For step function imperfections, the shear band is shown to be a step function, but it is shown that this solution is unstable.

scholarly journals Effects of Cyclic Freezing and Thawing on the Shear Behaviors of an Expansive Soil under a Wide Range of Stress Levels

2021 ◽  
Author(s):  
Wei-lie Zou ◽  
Zhong Han ◽  
Gui-tao Zhao ◽  
Kewei Fan ◽  
Sai K. Vanapalli ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Strain Softening ◽  
Expansive Soil ◽  
Friction Angle ◽  
Shearing Stress ◽  
Freezing And Thawing ◽  
Confining Stress ◽  
Stress Strain ◽  
Apparent Cohesion ◽  
Wide Range

Abstract The focus of this paper is directed towards investigating the influence of multiple freeze-thaw (FT) cycles on the stress-strain relationships during undrained shearing for an expansive soil under a wide range of confining stresses (σc) from 0 to 300 kPa. Different numbers of FT cycles were applied to compacted specimens. The influence of FT cycles on the soil’s structure was investigated using mercury intrusion porosimetry (MIP) and scanning electron microscope (SEM) tests. FT impacted specimens were subjected to consolidated undrained (CU) shear tests with pore pressure measurement (σc = 10 to 300 kPa) and unconfined compression (UC) tests (σc = 0 kPa) to derive the shearing stress-strain relationships and the associated mechanical properties including (i) failure strength (qu), elastic modulus (Eu), effective and apparent cohesion (c’ and c), and effective and apparent friction angle (ϕ’ and ϕ) obtained from CU tests and (ii) qu and reloading modulus (E1%) and stress (Su1%) at 1% strain obtained from UC tests. Testing results show that FT cycles mainly influence the soil’s macropores with diameters between 5 and 250 microns. Cracks develop during FT cycles and result in slight swelling which contributes to an increase in the global volume of the soil specimens. There is a significant reduction in the investigated mechanical properties after FT cycles. They typically achieve equilibrium after about 6 cycles. The shearing stress-strain curves transits from strain-softening to strain-hardening as the confining stress increases. An empirical model is developed to describe the strain-softening behavior of the specimens under low confining stresses. The model is simple to use and well describes all stress-strain curves obtained in this study that show strain-softening characteristics.

scholarly journals An Insight into Amorphous Shear Band in Magnetorheological Solid by Atomic Force Microscope

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4384
Author(s):  
Mohd Aidy Faizal Johari ◽  
Asmawan Mohd Sarman ◽  
Saiful Amri Mazlan ◽  
Ubaidillah U ◽  
Nur Azmah Nordin ◽  
...  
Keyword(s):  
Stress Relaxation ◽  
Shear Band ◽  
Shear Bands ◽  
Test Duration ◽  
Phase Imaging ◽  
Force Microscopy ◽  
Atomic Force ◽  
The Matrix ◽  
Relaxation Stress ◽  
Band Deformation

Micro mechanism consideration is critical for gaining a thorough understanding of amorphous shear band behavior in magnetorheological (MR) solids, particularly those with viscoelastic matrices. Heretofore, the characteristics of shear bands in terms of formation, physical evolution, and response to stress distribution at the localized region have gone largely unnoticed and unexplored. Notwithstanding these limitations, atomic force microscopy (AFM) has been used to explore the nature of shear band deformation in MR materials during stress relaxation. Stress relaxation at a constant low strain of 0.01% and an oscillatory shear of defined test duration played a major role in the creation of the shear band. In this analysis, the localized area of the study defined shear bands as varying in size and dominantly deformed in the matrix with no evidence of inhibition by embedded carbonyl iron particles (CIPs). The association between the shear band and the adjacent zone was further studied using in-phase imaging of AFM tapping mode and demonstrated the presence of localized affected zone around the shear band. Taken together, the results provide important insights into the proposed shear band deformation zone (SBDZ). This study sheds a contemporary light on the contentious issue of amorphous shear band deformation behavior and makes several contributions to the current literature.

Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sheng Yu-ming ◽  
Li Chao ◽  
Xia Ming-yao ◽  
Zou Jin-feng
Keyword(s):  
Finite Element ◽  
Principal Stress ◽  
Stress Condition ◽  
Strain Softening ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Strength Criterion ◽  
Surrounding Rock ◽  
Flow Rule ◽  
Finite Element Software

Abstract In this study, elastoplastic model for the surrounding rock of axisymmetric circular tunnel is investigated under three-dimensional (3D) principal stress states. Novel numerical solutions for strain-softening surrounding rock were first proposed based on the modified 3D Hoek–Brown criterion and the associated flow rule. Under a 3D axisymmetric coordinate system, the distributions for stresses and displacement can be effectively determined on the basis of the redeveloped stress increment approach. The modified 3D Hoek–Brown strength criterion is also embedded into finite element software to characterize the yielding state of surrounding rock based on the modified yield surface and stress renewal algorithm. The Euler implicit constitutive integral algorithm and the consistent tangent stiffness matrix are reconstructed in terms of the 3D Hoek–Brown strength criterion. Therefore, the numerical solutions and finite element method (FEM) models for the deep buried tunnel under 3D principal stress condition are presented, so that the stability analysis of surrounding rock can be conducted in a direct and convenient way. The reliability of the proposed solutions was verified by comparison of the principal stresses obtained by the developed numerical approach and FEM model. From a practical point of view, the proposed approach can also be applied for the determination of ground response curve of the tunnel, which shows a satisfying accuracy compared with the measuring data.

Plastic Deformation-Induced Nanocrystalline Aluminum in Al-Based Amorphous Alloys

1993 ◽  
Vol 321 ◽  
Author(s):  
H. Chen ◽  
Y. He ◽  
G. J. Shiflet ◽  
S. J. Poon
Keyword(s):  
Plastic Deformation ◽  
Amorphous Alloy ◽  
Shear Band ◽  
Thin Layer ◽  
Ball Milling ◽  
Direct Observation ◽  
Amorphous Alloys ◽  
Shear Bands ◽  
Amorphous Ribbons ◽  
Nanocrystalline Aluminum

ABSTRACTWe report the first direct observation of crystallization induced in the slipped planes of aluminum based amorphous alloys by bending the amorphous ribbons. Nanometer-sized crystalline precipitates are found exclusively within a thin layer (shear band) in the slipped planes extending across the deformed amorphous alloy ribbons. It is also found that the nanocrystalline aluminum can be produced by ball-Milling. It is likely that local atomic rearrangements within the shear bands create the nanocrystals which appear after plastic deformation.

Dynamic Failure Mechanisms in Beryllium-Bearing Bulk Metallic Glasses

1998 ◽  
Vol 554 ◽  
Author(s):  
David M. Owen ◽  
Ares J. Rosakis ◽  
William L. Johnson
Keyword(s):  
Crack Initiation ◽  
Shear Band ◽  
Metallic Glasses ◽  
Impact Loading ◽  
High Speed ◽  
Failure Mechanisms ◽  
Shear Bands ◽  
Dynamic Crack ◽  
Dynamic Failure ◽  
Asymmetric Impact

AbstractThe understanding of dynamic failure mechanisms in bulk metallic glasses is important for the application of this class of materials to a variety of engineering problems. This is true not only for design environments in which components are subject to high loading rates, but also when components are subjected to quasi-static loading conditions where observations have been made of damage propagation occurring in an unstable, highly dynamic manner. This paper presents preliminary results of a study of the phenomena of dynamic crack initiation and growth as well as the phenomenon of dynamic localization (shear band formation) in a beryllium-bearing bulk metallic glass, Zr41.25Ti13.75Ni10Cu12.75Be22.5. Pre-notched and prefatigued plate specimens were subjected to quasi-static and dynamic three-point bend loading to investigate crack initiation and propagation. Asymmetric impact loading with a gas gun was used to induce dynamic shear band growth. The mechanical fields in the vicinity of the dynamically loaded crack or notch tip were characterized using high-speed optical diagnostic techniques. The results demonstrated a dramatic increase in the crack initiation toughness with loading rate and subsequent crack tip speeds approaching 1000 m s−1. Dynamic crack tip branching was also observed under certain conditions. Shear bands formed readily under asymmetric impact loading. The shear bands traveled at speeds of approximately 1300 m s−1 and were accompanied by intense localized heating measured using high-speed full-field infrared imaging. The maximum temperatures recorded across the shear bands were in excess of 1500 K.

Stury of Post-Failure Constitutive Relation Based on SMP Criterion

2013 ◽  
Vol 790 ◽  
pp. 405-409
Author(s):  
Jian Ming Zhu ◽  
Ze Xiang Wu ◽  
Qi Zhao ◽  
Chong Yang
Keyword(s):  
Residual Stress ◽  
Elastic Modulus ◽  
Constitutive Model ◽  
Constitutive Relation ◽  
Strain Softening ◽  
Friction Angle ◽  
Peak Friction Angle ◽  
Confining Pressures ◽  
Intermediate Variables ◽  
Nonlinear Elastic

In this paper, based on SMP criteria, combination of strain softening of rock material mechanics theory, the after peak friction angleφfor the intermediate variables, the residual strainεto express the after peak nonlinear elastic modulusE, and finally establish a unified non-linear constitutive model of the rock peak residual stress. Combination Xiao Guanzhuang Eastern Mine typical breakdown rock of diorite triaxial test , get stress-strain curves for different confining pressures by this model. It shows that peak constitutive relation of this study can simulate the experimental results, prove the rationality of the model.

scholarly journals The influence of pavement degradation caused by cyclic loading on its failure mechanisms

2016 ◽  
Vol 11 (3) ◽  
pp. 179-187 ◽  
Author(s):  
Marcin Gajewski ◽  
Stanisław Jemioło
Keyword(s):  
Yield Condition ◽  
Limit Load ◽  
Flow Rule ◽  
Smooth Approximation ◽  
Simple Method ◽  
Plastic Properties ◽  
The Road ◽  
Plastic Materials ◽  
Number Of Cycles ◽  
Elastic Plastic Materials

In this paper, a simple method is proposed to estimate capacity of multilayered road structure including the degradation of the elastic and plastic properties of the constituent materials. In the study boundary value problem modeling interaction of wheels with road surface layer in the frame of large deformation theory for elastic-plastic materials was formulated. Plastic properties of the material were described by the flow rule un-associated with yield condition. The Coulomb-Mohr yield condition was assumed and the potential for plasticity is its smooth approximation. In addition, in constitutive modeling the dependence of the Young’s modulus and cohesion of the material from the number of cycles is taken into account. This paper presents qualitative findings in relation to mechanical behavior of the road structure, i.e., for example, the development of plastic zones with increasing load for un-degraded and degraded materials. In addition, a parametric study of the influence of the degradation ratio of the elasticity and plasticity properties for road structure failure mechanism (limit load value) was made.

Plane-Strain Crack-Tip Fields for Pressure-Sensitive Dilatant Materials

1990 ◽  
Vol 57 (1) ◽  
pp. 40-49 ◽  
Author(s):  
F. Z. Li ◽  
J. Pan
Keyword(s):  
Plane Strain ◽  
Effective Stress ◽  
Hydrostatic Stress ◽  
Yield Criterion ◽  
Crack Tip ◽  
Flow Rule ◽  
Pressure Sensitivity ◽  
Crack Tip Fields ◽  
Pressure Sensitive ◽  
Plane Strain Crack

Plane-strain crack-tip stress and strain fields are presented for materials exhibiting pressure-sensitive yielding and plastic volumetric deformation. The yield criterion is described by a linear combination of the effective stress and the hydrostatic stress, and the plastic dilatancy is introduced by the normality flow rule. The material hardening is assumed to follow a power-law relation. For small pressure sensitivity, the plane-strain mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, 1968a, b; Rice and Rosengren, 1968). The angular distributions of the fields depend on the material-hardening exponent and the pressure-sensitivity parameter. The low-hardening solutions for different degrees of pressure sensitivity are found to agree remarkably with the corresponding perfectly-plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on the crack-tip fields is the lowering of the hydrostatic stress and the effective stress directly ahead of the crack tip, which may contribute to the experimentally-observed enhancement of fracture toughness in some ceramic and polymeric composite materials.

scholarly journals Numerical Modelling of Soil Arching in a Shallow Backfill Layer

2015 ◽  
Vol 15 (4) ◽  
pp. 127-137 ◽  
Author(s):  
Waldemar St. Szajna
Keyword(s):  
Internal Friction ◽  
Flexible Structures ◽  
Friction Angle ◽  
Internal Friction Angle ◽  
Plasticity Condition ◽  
Flow Rule ◽  
The Finite Element Method ◽  
Soil Arching ◽  
Plain Strain ◽  
The Impact

Abstract The paper presents the application of the finite element method into the modelling of soil arching. The phenomenon plays fundamental role in soil-shell flexible structures behaviour. To evaluate the influence of arching on a pressure reduction, a plain strain trapdoor under a shallow layer of backfill was simulated. The Coulomb-Mohr plasticity condition and the nonassociated flow rule were used for the soil model. The research examines the impact of the internal friction angle and the influence of the backfill layer thickness on the value of soil arching. The carried out analyses indicate that the reduction of pressures acting on a structure depends on the value of the internal friction angle, which confirms the earlier research. For a shallow backfill layer however, the reduction is only a local phenomenon and can influence only a part of the structure.

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