Shear Band Patterns Research Articles

Influence of mesoscale properties on the mechanisms of plastic strain accommodation in plane strain dynamic deformation of concentric Ni-Al laminates

The paper presents results on the mechanisms of plastic strain accommodation of Ni-Al laminates composed of concentrically aligned thin foils processed at different conditions undergoing a high strain radial collapse in thick walled cylinder experiments. Numerical simulations were conducted to examine the influence of mesoscale parameters (layer size, defects in mesostructure, and ductility) on the mechanisms of large plastic strain accommodation (high amplitude cooperative buckling; high frequency, low amplitude buckling; and kinking) at high strain rates in pure shear (plane strain) conditions. These mechanisms are dramatically different than observed in solid ductile and brittle homogeneous materials where a pattern of shear bands is the major mode of strain accommodation. It was observed that the layer thickness and ductility greatly influenced the dominant mode of plastic strain accommodation. The number of apices was related to the layer thickness. The presence of defects mainly had a localized area of influence. Numerical simulations showed good qualitative agreement with the experiments and provided the ability to simulate additional mesoscale and material dependencies: the role of friction/bonding, relative layer sizes, and sample thickness.

Dynamic fragmentation induced by network-like shear bands in a Zr-based bulk metallic glass

Dynamic fragmentation induced by network-like shear bands is observed in a Zr-based bulk metallic glass subjected to impact loading, which is different from shear failure via one dominant shear band under quasi-static compression. Further, the influence of elastic strain energy on the evolution of shear bands is investigated. It is shown that the shear-band pattern occurring in one dominated mode or in multiple modes strongly depends on the loading rates. Dynamic fragmentation is due to the competition between the elastic strain energy driving a shear band and the dissipated energy along the shear band.

Localized deformation in sands and glass beads subjected to plane strain compressions

In order to investigate shear behavior of granular materials due to excavation and associated unloading actions, load-controlled plane strain compression tests under decreasing confining pressure were performed under drained conditions and the results were compared with the conventional plane strain compression tests. Four types of granular material consisting of two quartz sands and two glass beads were used to investigate particle shape effects. It is clarified that macro stress-strain behavior is more easily influenced by stress level and stress path in sands than in glass beads. Development of localized deformation was analyzed using photogrammetry method. It was found that shear bands are generated before peak strength and shear band patterns vary during the whole shearing process. Under the same test condition, shear band thickness in the two sands was smaller than that in one type of glass beads even if the materials have almost the same mean particle size. Shear band thickness also decreased with increase of confining pressure regardless of particle shape or size. Local maximum shear strain inside shear band grew approximately linearly with global axial strain from onset of shear band to the end of softening. The growth rate is found related to shear band thickness. The wider shear band, the relatively lower the growth rate. Finally, observed shear band inclination angles were compared with classical Coulomb and Roscoe solutions and different results were found for sands and glass beads.

Patterned Nonaffine Motion in Granular Media

Vortex-like flow patterns are often observed in experiments on granular media for which uniform strain is expected based on the loading boundary conditions. These deformations become apparent when the motion associated with uniform strain is subtracted from the total particle motion. Besides presenting an interesting phenomenon that begs explanation, these vortex patterns suggest multiscale structure for nonaffine motion as suggested by modern continuum theories. Further, the authors note that the rotational velocity field added to a uniform strain field produces a planar slip field. Thus, these structures are associated with the slip-band fields that eventually form, which are generally associated with bifurcations in the solution path of the governing partial differential equations. The authors present a procedure to extract these motion fields from discrete-element simulations along with conjugate forces associated with these motions. A key finding from the simulations is that the motions that eventually lead to shear band formation develop throughout the loading history rather than arising as a distinct bifurcation. Further, the pattern of rotational fields, and hence the shear banding pattern, are controlled by the boundary conditions. A question, only partly resolved here, is the origin of forces driving the rotational fields.

Influence of relative density, particle shape, and stress path on the plane strain compression behavior of granular materials

Two types of stress path-controlled plane strain compression tests were performed on both loose and dense specimens of angular and sub-angular sands and two rounded glass beads with different particle sizes. Digital image correlation method was used to analyze local deformation developments, especially shear band patterns. The material behavior in response to shearing has been found to be dependent on the relative density, particle shape, and stress path. The results of analysis on local deformation developments showed that the onset of shear bands occurred prior to their peak strengths in both dense and loose specimens. The growth rates of local maximum shear strain along a shear band were approximately consistent with an increasing global axial strain after the onset of shear band. The shear band width was influenced by both the mean particle size and the particle shape. The measured shear band inclination angles were in between those estimated by Coulomb’s and Roscoe’s formulas.

Strain localization and fabric evolution in sand

Strain localization is frequently observed in sand and is considered an important precursor related to major geohazards such as landslides, debris flow and failure of relevant geo-structures. This paper presents a numerical study on strain localization in sand, with a special emphasis on the influence of soil fabric and its evolution on the initiation and development of shear band. In particular, a critical state sand plasticity model accounting for the effect of fabric and its evolution is used in the finite element analysis of plane strain compression tests. It is found that the initiation of shear band is controlled by the initial fabric, while the development of shear band is governed by two competing physical mechanisms, namely, the structural constraint and the evolution of fabric. The evolution of fabric generally makes the sand response more coaxial with the applied load, while the structural constraint induced by the sample ends leads to more inhomogeneous deformation within the sand sample when the initial fabric is non-coaxial with the applied stress. In the case of smooth boundary condition, structural constraint dominates over the fabric evolution and leads to the formation of a single shear band. When the boundary condition is rough, the structural constraint may play a comparable role with fabric evolution, which leads to symmetric cross-shape shear bands. If the fabric is prohibited from evolving in the latter case, a cross-shape shear band pattern is found with the one initiated first by the structural constraint dominating over the second one. In all cases, significantly larger dilation and fabric evolution are observed inside the shear band than outside. The simulated shear band orientation coincides with the Roscoe’s angle for cases with high confining pressure and lies in between the Roscoe’s angle and Arthur’s angle for the low confining pressure cases.

Characterization of Shear Bands in Zr<sub>64.13</sub>Cu<sub>15.75</sub>Ni<sub>10.12</sub>Al<sub>10 </sub>and Zr<sub>65</sub>Cu<sub>15</sub>Ni<sub>10</sub>Al<sub>10 </sub>BMGs

Shear banding characterization of Zr64.13Cu15.75Ni10.12Al10and Zr65Cu15Ni10Al10BMGs was studied by using Rockwell indention method. Well-developed shear band pattern can be found for both BMGs after indentation. The significant difference in plastic deformation ability can be ascribed to different shear banding features.

Collective evolution dynamics of multiple shear bands in bulk metallic glasses

The collective behavior of multiple shear bands was investigated under in situ four-point bending tests of a Zr-based bulk metallic glass (BMG) over a wide range of sample scales. The self-organization of shear band pattern, characterized by shear band spacing and shear offset, is observed with the variation of sample size and bend curvature, which presents significant size effect and tension–compression asymmetry. To unveil these fundamental behaviors, an analytical model for the evolution dynamics of multiple shear banding is developed for BMGs. In this model, both micro-structural evolution and pressure sensitivity are taken into account by introducing a new law for the stress softening of BMGs within the framework of continuum mechanics; the collective evolution of shear bands is regarded as the coupling result of the structural softening, the momentum diffusion, and the energy conservation. Applying the proposed theoretical model to the bending deformation of BMGs, the analytical solutions of shear band spacing, shear offset and failure strain are obtained. The fundamental behaviors of multiple shear bands are uncovered, in line with the experimental observations: notable scaling laws are found in the evolution of shear band spacing and shear offset, and the inhomogeneous size effect of plasticity is revealed by a transition from weak to strong size-dependence of failure strain with decreasing sample thickness. To be further, a competing map of shear band nucleation and propagation is established based on energy dissipation. The underlying mechanism of these size dependent behaviors of multiple shear bands in BMGs is found to be ascribed to the energy dissipation competition between the nucleation and propagation of shear bands.

Active earth pressure shielding in quay wall constructions: numerical modeling

By designing a quay wall construction the calculation of the active earth pressure behind the sheet pile wall is often a problem. Measurements and FE-analyses have shown that the earth pressure on a sheet pile wall is shielded due to the dowel effect of the pile rows behind the sheet piling. In conventional calculations a higher friction angle is used to take the dowel effect into account. In this study, numerical modeling using the Coupled Eulerian–Lagrangian method has been carried out to investigate the shielding effect of pile rows on the active earth pressure in sand. The failure mechanisms have been illustrated using the shear band patterns at the limit state. Based on the Terzaghi’s arching theory a new approach has been developed to estimate the shielding effect.

Effect of ion irradiation on mechanical behaviors of Ti40Zr25Be30Cr5 bulk metallic glass

In this work, the effect of C4+ and Cl4+ ion irradiation with 25 MeV energy on the hardness and shear banding feature of Ti40Zr25Be30Cr5 bulk metallic glass was studied. Depth-sensing nanoindetation and microindentation were applied for characterizing the multiple-scaled hardness and shear band patterns during plastic deformation. It is shown that the Cl4+ ion irradiation leads to an obvious softening of the sample surface, and distinctly affects the serrated flow feature during plastic deformation. In contrast, C4+ ions have little effect on the hardness and shear band patterns. Besides, the mechanism for the change of the mechanical properties and plastic deformation behavior after ion irradiation was also discussed.

Deformation patterns in Zr-based and Ti-based metallic glasses under scratch processes

The plastic deformation features of Zr- and Ti-based bulk metallic glasses (BMGs) are investigated by scratch method under different applied load and scratch velocity. The results show that the two BMG systems exhibit quite different shear band features during scratch processes. Shear band branching are found in Ti-based BMG, and the branching are more prominent at high applied load and rate during the scratch process. In contrast, the Zr-based BMG shows primary shear band dominating pattern, which becomes more straight and regular at high load and rate. Furthermore, the effect of structural relaxation on the shear band feature during scratch tests is studied. It is found that relaxation gives rise to a distinct transition from primary shear band dominating pattern to a branching and irregular pattern in the Zr-based BMG. The mechanism of change of the shear band pattern is discussed in the view of free volume theory.

Localization patterns in sandbox-scale numerical experiments above a normal fault in basement

The finite element program ELFEN is used to study the effect of basement fault dip on the evolution of shear band patterns in unconsolidated sand. The material properties and boundary conditions of the model were chosen to correspond to generic sandbox experiments.Model results reproduce the range of structural styles found in corresponding sandbox experiments. With a basement fault dip of 60° and lower, a graben structure is formed, composed of a synthetic shear band followed by one or more antithetic shear bands. With a basement fault dip of 70° and steeper, a reverse (precursor) shear band forms first, followed by a synthetic, normal shear band that accommodates all further displacement. The dip of the synthetic shear band is close to the basement fault dip. For basement fault dips between 60° and 70°, we observe a transition in localization patterns. An analysis of the stress fields and velocity vectors in the model explains the first-order aspects of the relationships observed.We consider the observed ‘precursor-dominated’ and ‘graben-dominated’structural domains to be important components of normal fault systems in which the first order structural style and deformation patterns are only weakly dependent on the details of the rheology of the model materials and explore the interesting problem of the change in structural style from ‘precursor-dominated’ to ‘graben-dominated’structural domains above a normal fault in basement. We find similar structural domains in sandbox experiments for the same set of boundary conditions but with slightly different material properties, suggesting that the modeled patterns are robust within these two structural domains, (i.e. will occur over a range of similar material properties and boundary conditions).The results of this study contribute to our ability to validate numerical models against experiments in order to finally better simulate natural systems.

Deformation and fracture behaviors of Ti-based metallic glass under multiaxial stress state

The deformation and fracture behaviors of a Ti-based metallic glass (MG) under a multiaxial stress state were investigated using a small punch test. It was found that controlling both the initiation and propagation of a shear crack can significantly stabilize the plastic deformation of Ti-based MG by forming multiple shear bands and delaying the shear crack from reaching the critical crack length. Radial, circumferential and spiral shear band patterns and corresponding fracture modes were observed. The relationship between the shear band pattern and the stress state was established. This finding implies that a MG could be stabilized and become ductile in nature under suitable stress conditions.

Quasi-static crack tip fields in rate-sensitive FCC single crystals

In this work, the effects of loading rate, material rate sensitivity and constraint level on quasi-static crack tip fields in a FCC single crystal are studied. Finite element simulations are performed within a mode I, plane strain modified boundary layer framework by prescribing the two term (K − T) elastic crack tip field as remote boundary conditions. The material is assumed to obey a rate-dependent crystal plasticity theory. The orientation of the single crystal is chosen so that the crack surface coincides with the crystallographic (010) plane and the crack front lies along \([10\overline 1]\) direction. Solutions corresponding to different stress intensity rates \(\dot{{K}}\), T-stress values and strain rate exponents m are obtained. The results show that the stress levels ahead of the crack tip increase with \(\dot{{K}}\) which is accompanied by gradual shrinking of the plastic zone size. However, the nature of the shear band patterns around the crack tip is not affected by the loading rate. Further, it is found that while positive T-stress enhances the opening and hydrostatic stress levels ahead of crack tip, they are considerably reduced with imposition of negative T-stress. Also, negative T-stress promotes formation of shear bands in the forward sector ahead of the crack tip and suppresses them behind the tip.

Interface Constraints on Shear Band Patterns in Bonded Metallic Glass Films Under Microindentation

When using the bonded interface technique for indentation tests, the semicircular and radial shear bands can be observed on the top surfaces and bonded interfaces in bulk metallic glasses (BMGs). In addition to the stress relaxation effects at the bonded interface, indentation tests on bonded BMG films on the steel platen further demonstrate the effects of the film/substrate interface on shear band patterns. The understanding of these shear band patterns will help design internal constraints to confine shear bands and thus to prevent brittle failure of BMGs. In contrast to previous studies, which connect shear band directions to principal shear stress or effective stress, as in the Mohr–Coulomb model, this article adopts the Rudnick–Rice instability theory—shear bands are a result of loss of material stability but are not a yield phenomenon. Shear band directions depend on material constitutive parameters (including Poisson’s ratio, coefficient of internal friction, and dilatancy factor) and principal stresses. Consequently, internal constraints such as the bonded interface and film/substrate interface may redistribute the stress fields and thus affect the shear band propagation directions. Finite element simulations were performed to determine the contact stress fields using continuum plasticity model. It is found that semicircular shear bands on the bonded interface follow the direction of the second principal stress, while radial shear band patterns depend on the two in-plane principal stresses. With the presence of film/substrate interfaces, the radial shear bands will be “reflected” at the interface, and the semicircular shear bands change directions and end at the interface. It should be noted that the actual stress field differs from the continuum plasticity simulations because of the strain localizations associated with shear bands. To this end, an explicit history of shear band nucleation and propagation is simulated by the free volume model, which reproduces the change from radial to semicircular shear bands when interface relaxation is introduced. These predictions agree well with our experimental observations of microindentation tests on two Zr-based BMG films laterally bonded and placed on a steel platen.

Mechanical response of amorphous ZrCuTi/PdCuSi nanolaminates under nanoindentation

In this paper, the relationship between mechanical response and shear band evolution for ZrCuTi (ZCT)/PdCuSi (PCS) nanolaminates under nanoindentation is discussed. Comparing to the monolithic amorphous ZCT and PCS films, the ZCT/PCS nanolaminates exhibit enhanced hardness and a more homogenous deformation mode. Cross-sectional transmission electron microscopy observations show that the shear-band patterns beneath the indent in ZCT/PCS nanolaminates are irregular and convoluted, and appear to be a mixture of the semi-circular shear bands and radial shear bands.

Fractal nature of multiple shear bands in severely deformed metallic glass

We present an analysis of fractal geometry of extensive and complex shear band patterns in a severely deformed metallic glass. We show that the shear band patterns have fractal characteristics, and the fractal dimensions are determined by the stress noise induced by the interaction between shear bands. A theoretical model of the spatial evolution of multiple shear bands is proposed in which the collective shear bands slide is considered as a stochastic process far from thermodynamic equilibrium.

Effect of loading rate on crack tip fields in three point bend fracture specimen of FCC single crystal

In this work, the effect of impact loading on mode I stationary crack tip fields in a three point bend FCC single crystal fracture specimen is investigated using plane strain finite element analysis. The behavior of the single crystal is assumed to be elastic-perfectly plastic. The main objective is to examine the role of material inertia in influencing the stress levels as well as the pattern of slip and kink shear bands around the tip. The results show that under quasi-static loading high stress levels prevail ahead of the notch tip. However, the specimen suffers considerable loss of constraint under dynamic loading, particularly during the initial stages. This increases with loading rate J ˙ . Also significant spread of the plastic zone occurs in the forward sector ahead of the tip under impact loading which is akin to isotropic solids. The pattern of shear bands around the tip in the single crystal also changes with impact velocity. In rate dependent single crystals, a competition between rate sensitivity and material inertia is observed. Thus, while the former enhances the stresses near the tip, the latter tends to reduce them.

Revelation of the effect of structural heterogeneity on microplasticity in bulk metallic-glasses

In this article, the shear-banding behavior in bulk metallic-glasses (BMGs) is studied using a focused ion beam (FIB)-based nanoindentation method, which involves cylindrical nanoindentation of a FIB-milled BMG microlamella and is capable of revealing the subsurface shear-band patterns down to the submicron scale. The results of the current study on a Zr-based BMG clearly show that short shear bands, with the lengths of a few hundred nanometers, could be severely kinked before growing into a longer one, which implies that structural heterogeneity plays an important role in the microplasticity of BMGs. Furthermore, through the three-dimensional finite-element simulation combined with the theoretical calculation based on the Mohr–Coulomb law, it is found that the yield strengths exhibit a large scatter as a consequence of the structural heterogeneity when microplasticity occurs in the Zr-based BMG, which is consistent with our recent findings obtained from the microcompression experiments.

CHARACTERIZATION OF SHEAR BANDS IN TWO BULK METALLIC GLASSES WITH DIFFERENT INHERENT PLASTICITY

Shear banding characterization of Zr 64.13 Cu 15.75 Ni 10.12 Al 10 and Zr 65 Cu 15 Ni 10 Al 10 bulk metallic glasses (BMGs) with significant difference in inherent plasticity and quite similar chemical composition was studied by depth sensitive macroindentaion tests with conical indenter. Well-developed shear band pattern can be found for both BMGs after indentation. Distinct difference in the shear band spacing, scale of plastic deformation region and the shear band branching in the two BMGs account for the different plasticity.