Evolution Of Strain Fields Research Articles

S153 Impact of Zirconium Hydride Precipitates on Fracture of a Zirconium Alloy

Zirconium alloys are of major importance to the nuclear industry, with primary application as a structural material for the in-reactor environment. The formation of brittle hydrides in zirconium alloys results in a degradation of the mechanical properties of the component in which they form. Thus, the rate and characteristics of formation and the subsequent impact of these hydrides are critical factors in the determination of zirconium component service life. This is a three part study of hydrides in zirconium using high energy synchrotron x-ray diffraction. Part I characterized the mechanical response of zirconium hydride, in situ in a Zircaloy-2 matrix. This study provided quantitative data on the elastic response of the hydride, as well as load transfer and fracture of the hydride phase; confirmed with finite element and composite mechanics models. Part II studied the near crack tip behavior of unhydrided Zircaloy-2. Strain field evolution as a function of applied load as well as the initiation of crack tip twinning were characterized with 2D mapping techniques. Two material orientations relative to the parent texture were investigated in a fatigue precracked condition with the results compared to finite element models. Part III then build on the results of the mapping study to characterize the effects of hydrides in the vicinity of the crack tip. The aim is to quantify the influence of crack tip hydrides on the local strain field around the crack tip, and to characterize the internal strains in the crack tip hydrides themselves.

A model for the propagation of strain solitary waves in solids with relaxing atomic defects

A model for the propagation of nonlinear dispersive one-dimensional longitudinal strain waves in an isotropic solid with quadratic nonlinearity of elastic continuum is proposed by taking into account the interaction of the longitudinal displacements with the temperature field and the field of concentration of nonequilibrium (recombining) atomic point defects (vacancies and interstitial atoms). The governing nonlinear equation describing the evolution of the self-consistent strain fields is derived. It is shown that the thermoelastic effect on the strain waves manifests itself in the appearance of dissipative terms, which describe the heat transfer and the thermoelastic interaction caused by the strain-induced heat release due to the recombination of atomic defects. The equation that describes the evolution of the amplitude of nonlinear traveling localized waves with time in the single-wave approximation is derived, and on the basis of this equation, the damping increments of these waves are determined with allowance the dissipative losses. The influence of stress-induced decay of defect complexes on the evolution of nonlinear strain waves is considered.

Fatigue damage analysis in a duplex stainless steel by digital image correlation technique

ABSTRACTStrain field measurements by digital image correlation today offer new possibilities for analysing the mechanical behaviour of materials in situ during mechanical tests. The originality of the present study is to use this technique on the micro‐structural scale, in order to understand and to obtain quantitative values of the fatigue surface damage in a two‐phased alloy. In this paper, low‐cycle fatigue damage micromechanisms in an austenitic‐ferritic stainless steel are studied. Surface damage is observed in real time, with an in situ microscopic device, during a low‐cycle fatigue test performed at room temperature. Surface displacement and strain fields are calculated using digital image correlation from images taken during cycling. A detailed analysis of optical images and strain fields measured enables us to follow precisely the evolution of surface strain fields and the damage micromechanisms. Firstly, strain heterogeneities are observed in austenitic grains. Initially, the austenitic phase accommodates the cyclic plastic strain and is then followed by the ferritic phase. Microcrack initiation takes place at the ferrite/ferrite grain boundaries. Microcracks propagate to the neighbouring austenitic grains following the slip markings. Displacement and strain gradients indicate probable microcrack initiation sites.

Friction Stir Processed AA5182-O and AA6111-T4 Aluminum Alloys. Part 2: Tensile Properties and Strain Field Evolution

In this second part, a state-of-the-art digital image correlation (DIC) technique was used to compute true stress-true strain curves beyond diffuse necking for friction stir processed AA5182-O and AA6111-T4 aluminum alloys. Of particular interest were differences in key tensile properties, such as initial yield point, and ultimate tensile strength, between the base and friction stir processed materials. Tensile coupons cut from the same material used to investigate crystallographic texture via the electron backscatter diffraction technique in Part 1, were strained to failure in a miniature tensile stage. The evolution of two-dimensional strain fields in both the base and friction stir processed materials was explored with incremental and cumulative strain maps computed from digital grids superimposed on each image after testing was completed. The impact of friction stir processing on strain localization just prior to fracture was revealed through changes in incremental strain map contour profiles. It is suggested that grain size refinement due to friction stir processing has a prominent effect on strength, while texture plays a secondary role.

Relationship between strain localization and catastrophic rupture

In order to explore a prior warning to catastrophic rupture of heterogeneous media, like rocks, the present study investigates the relationship between surface strain localization and catastrophic rupture. Instrumented observations on the evolution of surface strain field and the catastrophic rupture of a rock under uniaxial compression were carried out. It is found that the evolution of surface strain field displays two phases: at the early stage, the strain field keeps nearly uniform with weak fluctuations increasing slowly; but at the stage prior to catastrophic rupture, a certain accelerating localization develops and a localized zone emerges. Based on the measurements, an analysis was performed with local mean-field approximation. More importantly, it is found that the scale of localized zone is closely related to the catastrophic rupture strain and the rupture strain can be calculated in accord with the local-mean-field model satisfactorily. This provides a possible clue to the forecast of catastrophic rupture.

A Study of Crack–inclusion Interactions and Matrix–inclusion Debonding Using Moiré Interferometry and Finite Element Method

Failure behavior of composite materials in general and particulate composites in particular is intimately linked to interactions between a matrix crack and a second phase inclusion. In this work, surface deformations are optically mapped in the vicinity of a crack–inclusion pair using moire interferometry. Edge cracked epoxy beams, each with a symmetrically positioned cylindrical glass inclusion ahead of the tip, are used to simulate a compliant matrix crack interacting with a stiff inclusion. Processes involving microelectronic fabrication techniques are developed for creating linear gratings in the crack–inclusion vicinity. The debond evolution between the inclusion–matrix pair is successfully mapped by recording crack opening displacements under quasi-static loading conditions. The surface deformations are analyzed to study evolution of strain fields due to crack–inclusion interactions. A numerical model based on experimental observations is also developed to simulate debonding of the inclusion from the matrix. An element stiffness deactivation method in conjunction with critical radial stress criterion is successfully demonstrated using finite element method. The proposed methodology is shown to capture the experimentally observed debonding process well.

Influence of fiber orientation on global mechanical behavior and mesoscale strain localization in a short glass-fiber-reinforced epoxy polymer composite during tensile deformation investigated using digital image correlation

Advanced polymer composites are used in various fields such as light-weight automobile, aerospace and bio-implant engineering owing to their extraordinary mechanical properties. The various fields of application and the complex microstructures of such materials require better understanding of their micromechanical behavior under external loads. In this work, the tensile testing is coupled with the novel technique of surface displacement mapping via digital image correlation (DIC) is utilized for resolving the mechanical behavior and spatial distribution of the plastic microstrains in an epoxy resin reinforced with 35 wt% short borosilicate glass fibers. The DIC method works by correlating the digital images of surface patterns before and after straining. The material exhibited a pronounced mechanical anisotropy at both macro and mesoscale, which depends on the alignment of the fibers relative to the external load. The underlying microstructure of the material explained formation of strain gradients during evolution of full-field strain fields. The levels of localized strain are higher than the global failure strain of the material. Also, scanning electron microscopy (SEM) on the fracture surfaces revealed the multiple failure mechanisms of the material as a function of the fiber orientation.

Four magmatic fabrics in the Tuolumne batholith, central Sierra Nevada, California (USA): Implications for interpreting fabric patterns in plutons and evolution of magma chambers in the upper crust

For the first time, four distinct magmatic fabrics are documented in a composite plutonic body, the Tuolumne batholith, central Sierra Nevada, California, USA. One type of fabric was formed by strain caused by highly localized magma flow (type 1), whereas the other three chamber-wide fabrics recorded strain increments during boundary processes along batholith margins (type 2) superimposed by increments of heterogeneous regional tectonic strain (types 3 and 4). Our present work indicates that, in contrast to studies that consider magmatic fabrics to be simple structures formed by a single process, magmatic lineations and foliations in plutons may reflect accumulated finite strain and form as composite structures recording multiple strain increments in relatively static, actively deforming and rheologically complex crystal mushes at lower melt percentages. We demonstrate that multiple magmatic fabrics in a single batholith may record remarkably different processes and thus preserve a temporal record of strain in the batholith from strain during internal chamber processes to postem-placement regional tectonic strain. However, it may be commonly very problematic to infer the exact nature of flow or even fabric-forming process from the preserved rock record. Our study also exemplifies how examination of magmatic fabric patterns in plutons, complemented with geochronology, may provide crucial constraints on the interplay among successive magma emplacement, fabric preservation, temporal evolution of strain fields in a crystallizing magma chamber, and the development of crystal-mush zones.

Strain localization in geomaterials

Abstract The main purpose of this paper is a broad review of developments in observation and interpretation of localization in geomaterials in the laboratory, with an emphasis on low mean stress situations. Laboratory investigation of strain localization in granular soils and rocks has been pursued extensively and very accurate strain field evolution measurement techniques have been developed, including false relief stereophotogrammetry (FRS) and computed tomography (CT). These permit full characterization of strain localization, from onset to complete shear band formation. This paper reviews studies of sand, clay, sandstone, stiff marl and concrete, and observations of incipient and developed localization in initially ‘homogeneous’ laboratory tests are presented. Development of localization and peak strength, critical stress and strain, shear band orientation and thickness, and complex localization patterns are discussed. Deformation during triaxial compression of sand is shown to develop complex strain localization patterns. Consequently, the critical void ratio concept in granular materials is reconsidered. Void ratio evolution, global and local, monitored by CT, shows a limiting void ratio being rapidly attained in the strain localization zones. In cohesive materials (clays, rocks and concrete), crack development is also commonly observed. Displacement discontinuity measurement techniques are presented and the results for different cohesive geomaterials are discussed.

Correlation between localized strain and damage in shear-loaded Pb-free solders

A digital image correlation (DIC) algorithm was employed to measure microscopic strain-field evolution in shear-loaded model solder interconnections made out of a number of Sn-based alloys. Four different solder alloys studied were Sn–36Pb–2Ag, Sn–3.8Ag–0.7Cu (SAC), Sn–3.3Ag–3.82Bi, and Sn–8Zn–3Bi. The measured strain fields were correlated with damage observed at the scale of the sample, and at microscopic length scales. Local strain differs significantly from applied global strain and has been shown to depend on the geometry of the samples as well as the microstructure (on a grain level) of the solder. Strain fields in all solder interconnections were found to localize near but not at the solder–substrate interface and along grain boundaries in the solders. The eventual failure path as observed on the scale of the sample (parallel to the two solder–substrate interfaces with a cross-over from one interface to the other somewhere in the connection) showed a good correlation with measured strain fields in all interconnections. In contrast to the similarity on a macroscopic scale, on a microscopic scale the failure mechanisms were observed to be material specific.

Effects of Changing Environment and Loading Speed on Mechanical Behavior of FRP Composites

Durability of fiber reinforced polymer composites (FRP) are controlled by the durability of their constituents: reinforcement fibers, resin matrices, and the status of interfaces. A great deal of research has been focused on attempting to assess the relationship between interfacial structure and properties of fiber-matrix composites. It is at the interfacial area where stress concentration develops because of differences in the thermal expansion coefficients between the reinforcement and the matrix phase. A significant mismatch in the environmentally induced degradation of matrix and fiber leads to the evolution of localized stress and strain fields in the FRP composite. The present investigation aims to study the effects of changing hygrothermal conditioning cycles (either by changing relative humidity (RH) and keeping the temperature constant, or by changing the temperature while RH the same is maintained) on moisture gain/loss kinetics and on interlaminar shear strength (ILSS) of varied weight fraction glass fiber reinforced epoxy and polyester matrices composites. The mechanical assessment is extended to evaluate the loading rate sensitivity of hygrothermally shocked glass/epoxy and glass/polyester laminates at 2 and 50 mm/min crosshead speeds, respectively. Observations on absorption/desorption kinetics are noticed to be dependent on the nature of hygrothermal shock cycle and on the weight fraction of fiber reinforcement. The results of mechanical performance are statistically significant at different stages of conditioning. Shear values are found to be greater at higher crosshead speed for all undertaken situations. Mechanical responses are observed to be dependent on the matrix resin and the type of hygrothermal shock cycle. Very little and limited literature is open to address the important interactions of polymer composites with this kind of realistic environmental situation.

Analysis of the spallation mechanism suppression in plasma-sprayed TBCs through the use of heterogeneous bond coat architectures

This paper critically examines the use of heterogeneous bond coats to increase the durability of plasma-sprayed thermal barrier coatings under spatially-uniform cyclic thermal loading. A major failure mechanism in these types of coatings involves spallation of the top coat caused by the top/bond coat thermal expansion mismatch concomitant with deposition-induced top/bond coat interfacial roughness, oxide film growth and creep-induced normal stress reversal at the rough interface’s peaks. The reduction of the top/bond coat thermal expansion mismatch aimed at increasing coating durability can be achieved by embedding alumina particles in the bond coat. Herein, we analyze the evolution of local stress and inelastic strain fields in the vicinity of the rough top/bond coat interface during thermal cycling, and how these fields are influenced by the presence of spatially uniform and non-uniform (graded) distributions of alumina particles in the metallic bond coat. The analysis is conducted using the higher-order theory for functionally graded materials which accounts for the high-temperature creep/relaxation effects within the individual TBC constituents. In the presence of two-phase bond coat microstructures, both the actual and homogenized bond coat properties are employed in the analysis in order to highlight the limitations of the prevalent homogenization-based approach applied to graded materials. The results reveal that the use of heterogeneous, two-phase bond coats, with spatially uniform or graded microstructures, while slightly suppressing the normal stress component evolution in the interfacial peak region, increases the magnitude of the shear stress component as well as the inelastic strain evolution in this region, thereby potentially promoting delamination initiation. The analysis based on homogenized bond coat microstructure produces misleading results relative to how the bond coat heterogeneity affects the magnitude of the normal and shear stress, and inelastic strain, components.

Origin of the in situ stress field in south‐eastern Australia

AbstractThe in situ stress field of south‐eastern Australia inferred from earthquake focal mechanisms and bore‐hole breakouts is unusual in that it is characterised by large obliquity between the maximum horizontal compressive stress orientation (SHmax) and the absolute plate motion azimuth. The evolution of the neotectonic strain field deduced from historical seismicity and both onshore and offshore faulting records is used to address the origin of this unusual stress field. Strain rates derived from estimates of the seismic moment release rate (up to ∼10−16 s−1) are compatible with Quaternary fault–slip rates. The record of more or less continuous tectonic activity extends back to the terminal Miocene or early Pliocene (10–5 Ma). Terminal Miocene tectonic activity was characterised by regional‐scale tilting and local uplift and erosion, now best preserved by unconformities in offshore basins. Plate‐scale stress modelling suggests the in situ stress field reflects increased coupling of the Australian and Pacific Plate boundary in the late Miocene, associated with the formation of the Southern Alps in New Zealand.

Crack instability in ductile materials analyzed by the method of interpolated ellipses

The subject of this work is the description of the experimental “method of interpolated ellipses” (MIE) and its application in fracture mechanics studies. The MIE is a new technique based on the optical monitoring of deformations during the loading processes of hexagonal grids of dots deposited on the surface of the monitored specimen. Loading the specimen deforms a cricle on the surface into an ellipse. Each ellipse is interpolated by six neighboring dots of the hexagonal grid. Knowledge of the ellipse parameters directly yields the magnitude and the direction of principal strains on the specimen surface. Principal strain evolution yields knowledge of evolution of the plastic strain field by numerical postprocessing. Experimental results obtained from fracture tests of specimens with varying constraint at the crack tip have proven the evolution of plastic strain field to be a discontinuous process. This has been shown to be especially the case at the decisive time interval just before crack instability occurs.

A full-field optical method for the experimental analysis of reinforced concrete beams repaired with composites

In this paper, four-point bending tests are conducted on Reinforced Concrete (RC) beams with flexural and shear deficiencies. Beams are repaired with externally bonded composite sheets. A full-field optical method, called the grid method, is utilized for measuring displacement fields over predefined areas of interest. The paper firstly describes the basic principle of the grid method. An effort is done for defining accurately the measurement resolution and the spatial resolution. Then, the grid method is applied onto RC beams repaired with Carbon-Fibre-Reinforced-Plastic (CFRP) sheets in flexure. A measurement of crack widths all along the crack length is achieved. Subsequently, crack bridging by the bonded CFRP sheet is characterized. Another example is given for a repair in shear. The grid method is utilized for measuring strain fields over a Glass-Fibre-Reinforced-Plastic sheet which is bonded onto cracked concrete. Strain concentrations are detected at the location of cracks. Moreover, the evolution of strain fields with increasing loads leads to an interpretation of failure mechanism. Finally, both examples prove the great potentiality of the grid method for a sharp characterization of structures containing cracks. The results obtained for shear and flexural strengthening with composites, are original.

Spherical nano-indentation of a hard thin film/soft substrate layered system: II. Evolution of stress and strain fields

The evolution of stress/strain fields during spherical nano-indentation of a Si hard film/Al soft substrate layered system was investigated numerically. Observation of the stress and strain fields for a small indenter radius suggested that critical indentation depths could be correlated with elastic stress field interaction with the substrate (for 2% load-error-tolerable limit) or plastic deformation in the substrate (for 10% load-error-tolerable limit). The stress field interaction with the substrate or plastic deformation of the substrate provided an earlier indication of error than the load–displacement curves when the indenter radius was small. However, when the indenter radius was large, the latter was more sensitive to errors during the indentation process. Evolution of strain fields beyond the critical indentation limit was also investigated and is discussed.

Mechanical Modeling and Characterization of the Curing Process of Underfill Materials

Thermo-setting polymers are widely used as underfill materials to improve the reliability of electronic packages. In the design phase, the influence of underfill applications on reliability is often judged through thermal and mechanical simulations, under assumed operating conditions. Because of lacking insight into the mechanical processes due to polymer curing, the impact of processing induced residual stress fields is often neglected. To investigate the evolution of stress and strain fields during the curing process it is important to assume a more appropriate starting point for subsequent process modeling. Furthermore, study of possible damage originating from the fabrication process then comes within reach. To facilitate future analysis of stress and strain fields during the curing process a cure dependent constitutive relation is assumed. An approximate investigation method for the process-dependent mechanical properties, based on Dynamic Mechanic Analysis (DMA), is developed. As an illustration the parameter identification is performed for a selected epoxy resin.

Migration of large earthquakes along the San Jacinto Fault; Stress diffusion from the 1857 Fort Tejon Earthquake

Historic and modern catalogs of seismicity in California suggest a migration of earthquakes (M ≥ 5.6) along the San Jacinto Fault; these events appear to travel down the fault with a migration speed of 1.7 km/year (Sanders [1993]). This migration is explained by postseismic strain diffusion due to viscoelastic relaxation from the great Fort Tejon earthquake in 1857. We model this postseismic effect and find that significant stress diffuses down the San Jacinto fault for distances in excess of 200 km and the corresponding migration may be a result of Coulomb triggering from this stress perturbation. The level of postseismic stress that seems to be the trigger level for most of the events is of order 1 bar. Since the temporal evolution of the postseismic strain field is mainly dependent on the inelastic properties of the lower crust and uppermost mantle, the observed migration enables a viscosity estimate of ∼4 × 1018 Pas for this region of California.

Relation between the evolution of seismic apparent strain field and the region of strong earthquake occurrence

In this paper, according to the data on the middle and strong earthquakes in China, we have preliminarily studied the relation between the characteristic of space-time evolution of the seismic apparent strain field and the regions of 31 macroseism events since 1955. The result shows that, there is a rather well correlation between the anomaly region of seismic apparent strain and the zone of macroseism event occurrence within the time range of one to about five years. The R value of the application of the abnormal region of seismic apparent strain to predicting the area of strong earthquake occurrence is 0.458, and the empirical possibility of forecasting the region of macroseism occurrence is 0.625, and so the forecasting effect is comparatively well. Finally, the main results obtained above are discussed preliminarily.

Mesostructure of the localization in prestrained mild steel

In polycrystals, strain localization, i.e., sets of narrow bands carrying a large amount of plastic deformation, corresponds to an instable phenomenon, frequently observed during cold forming processes. In order to simulate such processes and their effect on localization, changes in loading path were extensively investigated at macroscopic and microscopic scales, but only little information is available on the evolution on the local strain field during localization. The aim of this paper is to analyze the evolution of local strain fields within the macroscopic bands of localization and to describe an intermediate scale, called meso-scale. This evolution was investigated at the surface of the samples, thanks to microextensometry techniques developed within a scanning electron microscope (SEM). The studied material was a mild steel, prestrained in plane tension parallel to the rolling direction, then tested in uniaxial tension parallel to the transversal direction.