Strain Localization Mechanisms Research Articles

Strain localization and damage mechanisms during bending of AA6016 sheet

The bendability of AA6016 sheets is a critical parameter for many automotive applications. In this experimental study the origins of damage and its evolution are characterized using interrupted and in-situ bending tests to correlate microstructural evolution with damage development. Local strains were estimated by optical and scanning microscopy (EBSD). Together with the load-displacement plots, they provided a set of physical parameters characterizing crack initiation. In particular, it is shown that(1)crack initiation occurs at the maximum of the rigidity–displacement curve;(2)cracking is preceded by strain localization in the form of macro-shear bands which induce surface roughening. Local necking then occurs in some surface grains and leads to ductile intergranular crack propagation.The sequence of microscopic changes at the grain scale up to and beyond crack initiation have been characterized and quantified in terms of local grain strains, coarse intragranular slip and shear band evolution over several grains.

Morphology of multiscale defect structures and plastic strain localization during impact perforation of A6061 alloy targets

Mechanisms of plastic strain localization (PSL) and fracture localization (FL) during dynamic (impact) loading accompanied by “plug” formation are related to structural transitions in the ensemble of defects. A characteristic feature of these transitions in the A6061 alloy is the multiscale character of the resulting structures. It is established that two bands featuring multiscale invariance can exist, namely, the PSL and FL bands, the lengths of which depend on the impact velocity. The length of a deformed layer, in which strain is localized, has a clear tendency of growing toward the free surface of the target. The passage from the PSL to FL band is characterized by a sharp increase in the Hurst exponent.

Numerical and experimental estimation of thermomechanical fields heterogeneity at the grain scale of 316L stainless steel

Polycrystalline metallic materials are made of an aggregate of grains more or less well oriented with respect to the loading axis. During mechanical loading, the diversity of grain orientations leads to heterogeneous deformation and it is well known that most of the plastic work generated during the deformation process reappears in the form of heat whereas a certain proportion remains latent in the material and is associated with microstructure changes. To access the local stored energy, experimental and numerical energy balances are needed at a suitable scale. In this way experiments have already been done in-house on 316L stainless steel to monitor the evolution of temperature and deformation fields at the microstructural scale. The aim of the present study is now to develop a simplified numerical model, based on experimental observations and able to simulate the thermomechanical behavior, in order to provide a first assessment of the stored energy level and heterogeneity. Our model renders well the average thermomechanical behavior of the specimen and reveals a high heterogeneity of the stored energy at the microstructure scale. Better knowledge of the stored energy at this scale should improve our understanding of strain localization mechanisms.

Resonance structure and inelastic strain and defect localization in loaded media

The paper provides a review of basic concepts of nonlinear dynamics and certain results relevant to the physical mechanisms of strain localization and increase in localization scales in loaded media. It is shown that the mechanisms of the processes can be associated with stable resonances occurring in loaded solids. A loaded solid is considered as a system of many interacting atoms perturbed by an external force with a continuous frequency spectrum. The question put in the work is what frequencies from this continuous spectrum are selected by the perturbed nonlinear system of interacting atoms, i.e., what frequencies are found to be most stable. The structure of resonances is analyzed using Hamilton's approach and Kolmogorov-Arnold-Moser theory. It is demonstrated that nonlinear dynamics gives results that fully explain the experimentally found regularity of increasing localization scales and fits it in the universal principle of fractal divisibility of solids and media. According to this principle, the minimum scale is the lattice parameter of a loaded solid and each subsequent scale is the sum of the two previous scales. The results obtained by Kolmogorov-Arnold-Moser theory show that invariant tori with an irrational angular coefficient to ω = (1, (√5−1)/2) are most stable, and this gives the experimental regularity L n +1 = L n / L n −1 , where L n ∼ 1/ω n , and L n +l / L n ≈ (√5+1)/2 for the corresponding wavelengths (scales).

Erratum to: “Strain Localization Mechanism of Interfacial Failure in Steel/Concrete Specimens,” by Y. Zhao, Y. Xing, J. Y. Huang, and A. F. Jiang, Vol. 47, No. 3, pp. 301–312, 2011.

Erratum to: “Strain Localization Mechanism of Interfacial Failure in Steel/Concrete Specimens,” by Y. Zhao, Y. Xing, J. Y. Huang, and A. F. Jiang, Vol. 47, No. 3, pp. 301–312, 2011.

Strain localization mechanism of interfacial failure in steel fiber/concrete specimens

The full strain field near the interface of steel fiber/concrete in a half-mold specimen was measured using a combined method of pullout test and digital image correlation. The strain localization mechanism of the interfacial failure is discussed. The strain distributions near the interface at a straight fiber under different loads show that the interfacial shear failure has a distinct characteristic of intervals in time and space directly related to the strain localization, which makes the interfacial failure initiate, develop and transfer successively. In particular, the local strain distributions around pores near the straight fiber interface demonstrate that the strain changes its sign at the irregular parts of the pore where the initial debonding took place and the deformation path is affected by the pore.

Internal stress in block media as a factor responsible for interface strain activity. Estimation of excess tectonic stress

The paper studies the mechanisms of strain localization at the interfaces of structural elements in quasi-2D block-structured (plate) systems. The model plate system is the ice cover of the Lake Baikal. The emphasis in the paper is on analyzing the relationship between intraplate strains and interplate displacements. It is shown that the activation of convergent interplate displacements and the development of subduction zones in the ice cover are due to an increase in tensile intraplate stress, and this is consistent with the main mechanisms of tectonic processes in the lithosphere. Analysis of the stress distribution allows the conclusion that the deformation mechanisms in the block-structured ice cover fit the concept of plate tectonics. The obtained results make it possible to estimate the characteristic tectonic stress (2–10% of the plate strength) at which convergent interplate displacements are activated. It is found that in individual regions of the plate system, anomalously high internal stress (up to 20–30% of the plate strength) can be reached resulting in fragmentation of structural blocks and involvement of the thus formed interfaces in deformation. It is demonstrated that with the so high internal stress, the deformation at the interplate boundaries is far from typical, and this can be considered as a precursor of coming dynamic seismogenic events.

Effects of precipitate morphology on the notch sensitivity of ductile fracture in heat-treatable aluminum alloys

Precipitate morphology evolution (PME) has been achieved in an Al–Mg–Si alloy by using two-step aging treatment. The PME from spherical gradually to rod-/needle-like allows us to track the mechanical properties to the precipitate morphology. For comparison, precipitate content evolution (PCE) was also developed in this alloy using one-step aging treatment, where the shape of precipitates was kept almost the same of needle-like. Systematic experiments have been carried out to compare the effects of PME and PCE on the notch sensitivity of the ductile fracture. It is clearly shown that the alloys with PME exhibit ductility and fracture toughness much sensitive to the triaxial stress than those with PCE. Interesting phenomena have been observed that the PME causes ductility and fracture toughness to change in an inverse way, i.e., fracture toughness increasing with decreasing ductility. While the PCE causes ductility and fracture toughness to vary in the same way. The difference in notch sensitivity of ductile fracture between PME- and PCE-containing alloys has been rationalized by considering a competition effect between precipitate–dislocation interaction and precipitate–matrix deformation discrepancy as the dominant strain localization mechanism, which, as revealed from quantitative assessments, is modulated by the precipitate morphology.

First-order gradient damage theory

Taking the strain tensor, the scalar damage variable, and the damage gradient as the state variables of the Helmholtz free energy, the general expressions of the firstorder gradient damage constitutive equations are derived directly from the basic law of irreversible thermodynamics with the constitutive functional expansion method at the natural state. When the damage variable is equal to zero, the expressions can be simplified to the linear elastic constitutive equations. When the damage gradient vanishes, the expressions can be simplified to the classical damage constitutive equations based on the strain equivalence hypothesis. A one-dimensional problem is presented to indicate that the damage field changes from the non-periodic solutions to the spatial periodic-like solutions with stress increment. The peak value region develops a localization band. The onset mechanism of strain localization is proposed. Damage localization emerges after damage occurs for a short time. The width of the localization band is proportional to the internal characteristic length.

Structural rejuvenation in a bulk metallic glass induced by severe plastic deformation

Using high-energy X-ray diffraction we examined the atomic structure in bulk metallic glass samples which underwent severe plastic deformation by the high-pressure torsion (HPT) technique. We obtained the atomic pair distribution function (PDF) and determined the changes in the PDFs due to deformation. The observed changes in the PDF clearly show structural disordering, which suggests structural rejuvenation by heavy deformation. However, the changes cannot be explained simply in terms of creating excess free volume, and they indicate that much more extensive atomic rearrangements take place as a consequence of deformation. Also, we suggest that the observed structural change may well be an outcome of local heating due to deformation and may not directly provide the knowledge of the atomistic mechanism of strain localization.

Mechanisms of strain localization, crack initiation and fracture of polycrystalline copper in the VHCF regime

Development of areas with strain localization is regarded as first step of fatigue damage and failure. At small load amplitudes only very few such areas are generated, but their number increases with number of cycles, until all grains are covered by them. Slip bands become persistent (PSBs) during high enough numbers of cycles. Formation of numerous persistent slip bands together with deep intrusions or small stage I (mode II) shear cracks, however, is not sufficient to form a long and propagating crack and thus specimen failure below a specified strain/stress amplitude. Specimen fracture requires an approximately 100% higher cyclic load than generating PSBs. The threshold value for PSB formation is lower than traditionally reported. Quantitative results on cyclic plastic strain measurements, TEM observations of the dislocation structure in the VHCF regime and determination of the critical crack length by use of a Kitagawa diagram are reported. Its relevance for fracturing and endurance limit is discussed.

Effect of precipitate morphology evolution on the strength–toughness relationship in Al–Mg–Si alloys

Experimental results show that the gradual evolution of precipitate morphology in Al–Mg–Si alloys, from spherical to rod-/needle-shaped, leads to an increase in ductility but a decrease in both yield strength and fracture toughness. The strength–ductility relationship reported here is similar to general observations but the strength–toughness relationship is distinctly different from the conventional one. These relationships are rationalized by considering a competition between dislocation–precipitate interaction and precipitate–matrix deformation discrepancy as the dominant strain localization mechanism, which is modulated by the evolution of precipitate morphology.

An Assessment of Compressive Size Effect of Plane Concrete Using Combination of Micro-Plane Damage Based Model and 3D Finite Elements Approach

In recent years, the material behavior dependence of laboratory concrete specimens built with the same concrete mixture under the same load conditions to their geometrical sizes is well established. This phenomenon which is observed not only in concrete but also in most quasi-brittle materials such as rock, ceramic or composite materials is now called as size effect. Many of the existing structural analyzing codes are not able to consider this important feature of concrete structures especially under compressive loadings. However we know that the main purpose of concrete application in structural members is to resist compression. The aim of this study is to show the ability of author's recently developed 3D finite elements code equipped with the proposed author's newly micro-planes damage based model for considering of compressive size effect of plane concrete. To do so, two different sizes of cubic concrete specimens are modeled with mentioned code under the uniaxial compressive test and their fracture mechanisms, pre-peak and post-peak strain-stress paths are investigated. Obtained results reveal the good coincidence with experimental evidences. In fact, the combination of proposed micro-planes damage based model and developed presented 3D finite elements technique creates a powerful numerical tool to capture and predict precisely strain localization and fracture mechanism in the specimens and consequently to assess properly the compressive size effect of plane concrete in analysis and design.

Using network analyses within geographic information system technologies to quantify geometries of shear zone networks

Shear zones often exhibit anastomosing network geometries. Previous work has shown that the detailed geometries of shear zone networks may partially control strain localization, fluid flow, rheology, and deformation mechanisms. However, there are currently no reliable tools to quantify network geometries such as the distribution of individual small shear zones and the connectedness of the network. Geographic information systems (GIS) provide a potential method for quantifying network geometries. GIS-based networking analyses have been used to quantify many different types of other networks, and here they are applied to shear zones. Many parameters within GIS-based networking analyses are useful for quantifying shear zone network geometries, including the connectivity parameters gamma and alpha, sinuosity, and vertex distribution patterns. Sets of these parameters are useful to quantitatively distinguish geometrical patterns of shear zone networks over a variety of conditions. Further quantification of shear zone network geometries may allow us to link those geometries to shear zone mechanisms, strain accumulation, and rheology.

Three-dimensional strain localization of water-saturated clay and numerical simulation using an elasto-viscoplastic model

Since strain localization is a precursor of failure, it is an important subject to address in the field of geomechanics. Strain localization has been analysed for geomaterials by several researchers. Many of the studies, however, treated the problems brought about by strain localization as two-dimensional problems, although the phenomena are generally three-dimensional. In the present study, undrained triaxial compression tests using rectangular specimens and their numerical simulation are conducted in order to investigate the strain localization behaviour of geomaterials under three-dimensional conditions. In the experiments, both normally consolidated and over-consolidated clay samples are tested with different strain rates. Using the distribution of shear strain obtained by an image analysis of digital photographs taken during deformation, the effects of the strain rates, the dilation, and the over-consolidation on strain localization are studied in detail. The analysis method used in the numerical simulation is a coupled fluid-structure finite element method. The method is based on the finite deformation theory, in which an elasto-viscoplastic model for water-saturated clay, which can consider structural changes, is adopted. The results of the simulation include not only the distribution of shear strain on the surfaces of the specimens, but also the distributions of strain, stress, and pore water pressure inside the specimens. Through a comparison of the experimental results and the simulation results, the mechanisms of strain localization are studied under three-dimensional conditions.

Deformation mode map of irradiated 316 stainless steel in true stress–dose space

Microscopic and macroscopic deformation modes in type 316 stainless steels after low-temperature irradiation have been mapped into the true stress–dose coordinate system. This paper defines and explains the deformation modes in 316 and 316LN stainless steels and suggests the procedures to produce a deformation mode map. A variety of microstructural features such as dislocation tangles and pileups, dislocation channels, stacking faults, and twins have been observed in the deformation of irradiated stainless steels. Attempts were also made to depict macroscopic phenomena such as uniform deformation, necking, and final fracture in the map. Stress criteria for twinning, channeling, plastic instability, and final failure were proposed and used to establish boundaries between the different deformation modes. Two alternative strain localization mechanisms, twinning and channeling, shared the high-dose region. The region of stable plastic deformation became narrower as dose increased, while the elastic deformation region was enlarged with dose and the unstable deformation region was kept unchanged over the whole dose range.

Localized strain autowaves at the initial stage of plastic flow in single crystals

Plastic strain localization in single crystals of pure metals and alloys is studied on the yield plateau and at the easy glide stage with a zero or small strain hardening coefficient. The difference between localization patterns in the two cases is explained, and strain localization mechanisms are suggested. At these stages of plastic deformation, various types of autowaves are observed.

Analysis of strain localization during tensile tests by digital image correlation

This paper presents an imaging technique developed to study the strain localization phenomena that occur during the tension of thin, flat steel samples. The data are processed using digital speckle image correlation to derive the two in-plane components of the displacement vectors. The authors observe that the calculation of the intercorrelation function reveals a systematic error and propose a numerical method to limit its influence. Plastic incompressibility and thin-sheet assumptions are used to derive the third displacement component and, hence, the various strain and strain rate components. Numerous checks are presented at each step in processing the data to determine the final accuracy of the strain measurements. It is estimated that this accuracy is quite sufficient to track the inception and the development of localization. Examples of possible application are presented for mild steels whose strain localization mechanisms appear to be precocious and gradual.

Erosive wear and impact damage of high-chromium white cast irons

High-chromium white cast irons are used extensively in environments where small particle impact causes considerable damage. In this study, three white cast irons with a variation in carbide volume fraction were eroded by spherical and angular particles. The white cast irons eroded at a higher rate when the erodent was WC–Co spheres than when the erodent was alumina particles. When eroded by spherical WC–Co particles, the eutectic white cast iron eroded at a higher rate than the hypoeutectic white cast iron. The results of the erosion experiments were interpreted in terms of a mechanism of platelet formation involving strain localization. The greater strain hardening rate of the hypoeutectic white cast iron can account for the better erosion resistance compared to the eutectic white cast iron, based on the strain localization mechanism. The larger size and greater density of the WC–Co spheres can account for the higher erosion rates of the white cast irons when eroded with WC–Co spheres compared to the erosion rate with alumina particles.

Strain localization mechanisms in deep-seated layered rocks

More than 160 shear zones of the Norwegian Caledonides and Italian Southern Alps, formed under high-temperature or high-pressure conditions, are analysed with respect to mechanisms of strain localization. In metabasic rocks with a pre-existing (magmatic) layering strain localizes preferentially in mafic layers, although experiments in monomineralic rocks would predict a location in the weaker feldspar-rich layers. In addition, in some of these zones amphibole recrystallizes dynamically, whereas feldspars only show undulatory extinction. These are evidences for strength inversion between feldspars and mafic minerals. This inverse strength behaviour is caused by a reduced grain size of feldspars and sometimes amphiboles in the pre-existing mafic layers, i.e. prior to shearing. The localization of the shear zones is therefore a grain-size-sensitive process (grain-size-dependent softening), nearly independent of the composition of the deformed material. The numerous amphibole–amphibole contacts favour dynamical recrystallization by grain-boundary migration and the rare feldspar–feldspar contacts prevent or suppress the same process in feldspars. Therefore, the feigned inverse strength is mainly caused by the interaction of reduced grain size and grain-boundary effects in the original rock. This behaviour can lead to the preferential localization of shear zones in mafic layers, although they are not favourably oriented with respect to the stress system.