Average Shear Strain Research Articles

Simulating soil stiffness degradation in transient site response predictions

A series of nonlinear seismic ground response analyses are conducted to investigate the effect of soil degradation on the seismic response of typical sedimentary deposits in Southern California. For this purpose, three downhole array station sites at the Los Angeles basin are subjected to broadband synthetic ground motion excitations. A characteristic strain measure, defined as the averaged maximum shear strain in the top 30 m of the soil profile ( γ 30 ), is proposed to enable the correlation between the ground shaking intensity level (here measured by means of the peak ground acceleration on the surface of rock-outcrop, PGA RO ) and the average deviation in ground motion response spectral predictions (denoted as e SA ) attributed to the effect of modulus degradation due to cyclic loading. It is shown that strong linear correlations exist among log ( PGA RO ) , log ( γ 30 ) and log ( e SA ) for the sites investigated. On the other hand, the number of loading cycles typically employed to indicate the importance of soil degradation is shown to play a much less important role. This becomes more apparent for near-field large amplitude ground motions characterized by a dominant pulse and overall low number of cycles, which nonetheless impose strains large enough to trigger modulus degradation effects. Based on this observation, it is suggested that the soil degradation effect in seismic ground motion is primarily controlled by the ground shaking intensity. The level of PGA RO beyond which soil degradation should be accounted for and incorporated in seismic ground response analysis is also depicted for the sites investigated.

A method for calculating damage evolution in adiabatic shear band of titanium alloy

A method for calculating the evolution of the local damage variable at the adiabatic shear band (ASB) center was proposed. In the present method, the JOHNSON-COOK model and the nonlocal theory were adopted, and the damage variable formula applicable for the bilinear (linearly elastic and strain-softening) constitutive relation was further generalized to consider the plastic deformation occurring in the strain-hardening stage. Aiming at Ti-6Al-4V, the effect of strain rate on the evolution of the local damage variable at the ASB center was investigated. In addition, a parametric study was carried out, including the effects of strain-hardening exponent, strain rate sensitive coefficient, thermal-softening exponent, static shear strength, strain-hardening modulus, shear elastic modulus, work to heat conversion factor, melting temperature and initial temperature. The damage extent at the ASB center in the radial collapse experiment was assessed. It is found that at higher strain rates the damage in the ASB becomes more serious at the same average plastic shear strain of the ASB.

Microstructure-Dependent Local Strain Behavior in Polycrystals through In-Situ Scanning Electron Microscope Tensile Experiments

Digital image correlation of laser-ablated platinum nanoparticles on the surface of a polycrystalline metal (nickel-based superalloy Rene 88DT) was used to obtain the local strain behavior from an in situ scanning electron microscope tensile experiment at room temperature. By fusing this information with crystallographic orientations from EBSD, a subsequent analysis shows that the average maximum shear strain tends to increase with increasing Schmid factor. Additionally, the range of the extreme values for the maximum shear strain also increases closer to the grain boundary, signifying that grain boundaries and triple junctions accumulate plasticity at strains just beyond yield in polycrystalline Rene 88DT. In situ experiments illuminating microstructure-property relationships of this ilk may be important for understanding damage nucleation in polycrystalline metals at high temperatures.

Interfacial shear strength in abalone nacre

The shear strength of the interface between tiles of aragonite in the nacre of red abalone Haliotis rufescens was investigated through mechanical tensile and shear tests. Dog-bone shaped samples were used to determine the tensile strength of nacre when loaded parallel to the plane of growth; the mean strength was 65 MPa. Shear tests were conducted on a special fixture with a shear gap of 200 μm, approximately 100 μm narrower than the spacing between mesolayers. The shear strength is found to be 36.9±15.8 MPa with an average maximum shear strain of 0.3. Assuming the majority of failure occurs through tile pull-out and not through tile fracture, the tensile strength can be converted into a shear strength of 50.9 MPa. Three mechanisms of failure at the tile interfaces are discussed: fracture of mineral bridges, toughening due to friction created through nanoasperities, and toughening due to organic glue. An additional mechanism is fracture through individual tiles.

Microstructure sensitivity of fretting fatigue based on computational crystal plasticity

Three-dimensional finite element simulations are conducted to study the effects of microstructure on the fretting fatigue behavior of duplex Ti–6Al–4V. These fretting simulations involve a rigid cylindrical indenter pressed on the half space of Ti–6Al–4V with different realizations of microstructure. The deformation behaviors of the primary α and α/β lamellar phases at room temperature are described by three-dimensional crystal plasticity constitutive relations. Microstructure attributes considered in this sensitivity study include crystallographic texture, grain size, and grain size distribution. Voronoi tessellation is used to construct the three-dimensional finite element models with various grain size distributions. The plastic strain behaviors and the distribution of the average maximum plastic shear strain among grains are analyzed and contrasted. The relative susceptibility for crack formation, including effects of various microstructure features, is determined using the Fatemi–Socie parameter. The results suggest that both average grain size and especially crystallographic texture have more influence on the plastic deformation and fretting fatigue behavior than grain size distribution for the fretting condition considered.

Constitutive properties of clayey fault gouge from the Hanaore fault zone, southwest Japan

Velocity step tests at a range of slip rates (0.0154–155.54 μm s−1) are performed using natural fault gouge containing smectite, mica, and quartz collected from an outcrop of the Hanaore Fault, southwest Japan. Field and microscopic observations reveal that the shear deformation is localized to a few centimeters or thinner layer of black clayey fault gouge. This layer is formed by multiple stages, and determining the width of the shear zone due to a single event is difficult to determine. The experimental data on the abrupt jumps in the load point velocity are fitted by a rate‐ and state‐dependent frictional law, coupled with the spring‐slider model, the stiffness of which is treated as a fitting parameter. This treatment is shown to be essential to determine the constitutive parameters and their errors. The velocity steps are successfully fit with typically two state variables: larger b1 with shorter dc1 and smaller b2 with longer dc2. At slip rates higher than 1 μm s−1, negative b2 is required to fit the data in most of the cases. Thin gouge layers (∼200 μm) in the experiment enables us to simulate large averaged shear strain which is important to recognize the evolution of the state variable associated with negative b2 and long dc2. Observation of microscopic structure after experiments shows poor development of Y planes. This may be consistent with the mechanical behavior observed: weak occurrence of initial peak strength at yielding and displacement hardening throughout the experiments.

Particle Image Velocimetry Study of Turbulence Characteristics in a Vessel Agitated by a Dual Rushton Impeller

Particle Image Velocimetry (PIV) has been used to investigate turbulence characteristics in a 0.48 m diameter stirred vessel filled to a liquid height ( H = 1.4 T) of 0.67 m. The agitator had dual Rushton impellers of 0.19 m diameter ( D = 0.4 T). The developed flow patterns depend on the clearance of the lower impeller above the base of the vessel, the spacing between the two impellers, and the submergence of the upper impeller below the liquid surface. Their combinations can generate three basic flow patterns, named, parallel, merging and diverging flows. The results of velocity measurement show that the flow characteristics in the impeller jet flow region changes very little for different positions. Average velocity, trailing vortices and shear strain rate distributions for three flow patterns were measured by using PIV technique. The characteristics of trailing vortex and its trajectory were described in detail for those three flow patterns. Since the space-resolution of PIV can only reach the sub-grid rather than the Kolmogorov scale, a large-eddy PIV analysis has been used to estimate the distribution of the turbulent kinetic energy dissipation. Comparison of the distributions of turbulent kinetic energy and dissipation rate in merging flow shows that the highest turbulent kinetic energy and dissipation are both located in the vortex regions, but the maxima are at somewhat different locations behind the blade. About 37% of the total energy is dissipated in dual impeller jet flow regions. The obtained distribution of shear strain rate for merging flow is similar to that of turbulence dissipation, with the shear strain rate around the trailing vortices much higher than in other areas.

A geometric model of fault zone and fault rock thickness variations

The thicknesses of fault rock and fault zones and the fault normal separations for breached and intact relay zones each show a positive correlation with fault displacement. The displacement to thickness ratio, or average shear strain, varies for the different structures increasing from intact relay zones (median value = 0.27) to fault rocks (median value = 50). The correlation for fault rocks is widely interpreted as a growth trend controlled by fault rock rheology, but the progression of displacement to thickness ratios for the different structures suggests an alternative model. In this alternative model a fault initiates as an array of irregular fault segments. As displacement increases, relay zones separating fault segments are breached and fault surface irregularities are sheared off, to form fault zones containing lenses of fault-bounded rock. With further displacement these lenses are progressively comminuted, and ultimately converted to zones of thickened fault rock. The final fault rock thickness is therefore influenced strongly by fault structure inherited from the geometry of the initial fault array. The large scale range on which fault segmentation and irregularities occur provides the basis for application of this model over a scale range of at least 7 orders of magnitude.

A New Shear-Compression-Specimen for Determining Quasistatic and Dynamic Polymer Properties

A new design of the shear compression specimen (SCS) for investigating the viscoelastic shear response of polymers is presented. The specimen consists of a polymer gage section with two metal ends that remain essentially rigid during deformation. Two closed-form analytic models are developed to predict the average stress and strain in the gage section from the deformation-load histories. This new SCS design and its analytic models are thoroughly evaluated via laboratory measurements and numerical simulations. These simulations show that the deformations in the gage section are more uniform than in the original design, and the distribution of the average shear stress and strain are highly homogenous. The simulation results yield good agreement with those of closed-form analytic results and the experiments demonstrate that the new SCS geometry and its analytic models are as reliable as other commonly employed specimens. It can also generate higher strain rates under usual loading conditions because of its smaller specimen gage length. The need for care in specimen preparation is also discussed in detail as illuminated by the experimental and simulation results.

Strain distribution over plaques in human coronary arteries relates to shear stress

Once plaques intrude into the lumen, the shear stress they are exposed to alters with hitherto unknown consequences for plaque composition. We investigated the relationship between shear stress and strain, a marker for plaque composition, in human coronary arteries. We imaged 31 plaques in coronary arteries with angiography and intravascular ultrasound. Computational fluid dynamics was used to obtain shear stress. Palpography was applied to measure strain. Each plaque was divided into four regions: upstream, throat, shoulder, and downstream. Average shear stress and strain were determined in each region. Shear stress in the upstream, shoulder, throat, and downstream region was 2.55+/-0.89, 2.07+/-0.98, 2.32+/-1.11, and 0.67+/-0.35 Pa, respectively. Shear stress in the downstream region was significantly lower. Strain in the downstream region was also significantly lower than the values in the other regions (0.23+/-0.08% vs. 0.48+/-0.15%, 0.43+/-0.17%, and 0.47+/-0.12%, for the upstream, shoulder, and throat regions, respectively). Pooling all regions, dividing shear stress per plaque into tertiles, and computing average strain showed a positive correlation; for low, medium, and high shear stress, strain was 0.23+/-0.10%, 0.40+/-0.15%, and 0.60+/-0.18%, respectively. Low strain colocalizes with low shear stress downstream of plaques. Higher strain can be found in all other plaque regions, with the highest strain found in regions exposed to the highest shear stresses. This indicates that high shear stress might destabilize plaques, which could lead to plaque rupture.

Half-cycle slip activity of persistent slip bands at different stages of fatigue life of polycrystalline nickel

The slip activity of persistent slip bands (PSBs) in polycrystalline nickel was studied using scanning electron microscopy (SEM) and atomic force microscopy (AFM). The half-cycle slip activity as well as the local shear strain amplitudes was investigated after half-cycle deformation at different numbers of cycles in the domain of stress saturation. Moreover, the fraction of grains containing cumulated PSBs and the accumulated volume fraction of PSBs was estimated depending on the number of cycles during fatigue life. The volume fraction of active PSBs during half-cycle deformation is significantly lower than the cumulated PSB volume and decreases with increasing number of cycles. Additionally, an increasing localization of cyclic plastic strain within the PSBs was observed. However, with increasing number of cycles the average local shear strain amplitude remains almost unchanged. Thus, PSBs in polycrystals are subjected to a life history which is characterized by active and inactive periods of their half-cycle slip activity during cyclic deformation at different stages of the saturation state.

Characterization of In-Plane Shear Properties of Laminated Composites at High Strain Rates

The in-plane shear responses of continuous fiber reinforced composite materials under high strain rates were characterized experimentally. The V-notch rail shear configuration was used for characterizing the in-plane shear behavior of Newport NB321/3k70 plain weave carbon fabric/epoxy, NCT/321/G150 Carbon Fiber Unitape/epoxy, NB321/7781 fiberglass/epoxy, Cytec PWC/T300/3KNT plain weave carbon fabric/epoxy and Fibercote 3KPW/E365 plain weave carbon fabric/epoxy systems. The testing was conducted using a servo hydraulic testing machine at nominal stroke rates ranging between 0.00083in/sec to 500in/sec. A maximum average shear strain rate of 654rad/sec was achieved up to shear strain levels of 0.08 radians, during the tests. The stress-strain behavior of all material systems exhibited contrasting behavior with increasing stroke rates. The stress-strain curves for all materials exhibited an asymptotic behavior for stroke rates approaching 10in/sec and were material dependent for stroke rates exceeding 250in/sec. For Newport NB321/3k70 and NB321/7781 systems at the highest test rate, the shear strengths increased by a factor of three relative to that of the quasi-static rate, and were independent of the reinforcement type. The shear strength for Cytec PWC/T300/3KNT, Fibercote 3KPW/E365 and Newport NCT/321/G150 increased until a stroke rate of 100in/sec and later decreased with increasing stroke rate. The failure modes for Cytec PWC/T300/3KNT, Fibercote 3KPW/E365 and Newport NCT/321/G150 were at the minimum section of the shear coupons, while for Newport NB321/3k70 and NB321/7781, failure was observed to change from a shear mode across the minimum section to a complex failure mode away from the minimum section.

A Study on the Thermal Fatigue Behavior of Solder Joints Under Power Cycling Conditions

Failure mechanisms exposed by environmental accelerating testing methods such as thermal cycling or thermal shock test, may differ from those at service operating conditions. While the device is heated up or cooled down evenly on its external surface during environmental testing, real operating powered devices experience temperature gradients caused by internal local heating, components' different heat dissipation capability, and ambient temperature variation, etc. In this study, a power cycling technique is introduced to better approximate the field operating conditions so as to activate the field failure modes. Power cycling thermal fatigue test is performed with different ball grid array solder joints, that is, lead contained [Sn/37 Pb (SP)] and lead free [Sn/4.0Ag/0.5 Cu (SAC)], and the result is compared. In order to account for the thermal fatigue life behavior discrepancy for different solder joint composition, real time Moire interferometry is applied to measure the global/local thermo-mechanical behavior during power cycling excursion. Effective damage parameter, the total average shear strain, is extracted from the experiment and applied to account for the difference in fatigue life result of two different solders. In addition, amount of experimentally measured total average shear strain is mutually verified with finite element method analysis. It is clear that total average shear strain of a solder joint can be an effective damage parameter to predict thermo-mechanical fatigue life. A physical mechanism in terms of thermal material property of solder joints' is proposed to offer some thoughts to abnormal shear strain behavior that leads to discrepancies in fatigue life of two solders. An importance of power cycling testing method is emphasized for certain package designs.

Peak and Average Temperatures in Adiabatic Shear Band for Thermo-Viscoplastic Metal Materials

Gradient-dependent plasticity considering the microstructural effect is introduced into Johnson-Cook model to calculate the nonuniform temperature distribution in adiabatic shear band (ASB) and the evolutions of average and peak temperatures in ASB. Effects of initial static yield stress, strain-hardening coefficient, strain-hardening exponent, strain-rate parameter and thermal-softening parameter are numerically investigated. The calculated peak temperature in ASB considering both the plastic work and the microstructural effect is always greater than the average temperature calculated only using the plastic work. For much lower flow shear stress, the peak temperature approaches two times the average temperature. The occurrence of phase transformation in ASB is easier in metal material with higher initial static yield stress, strain-hardening coefficient, strain-rate parameter and thermal-softening parameter. At much lower flow shear stress or much higher average plastic shear strain, the phase transformation occurs more easily in material with a lower strain-hardening exponent. Traditional elastoplastic theory without the microstructural effect underestimates the peak temperature in ASB so that the experimentally observed phase transformations cannot be explained.

Adiabatic Shear Localization for Steels Based on Johnson-Cook Model and Second- and Fourth-Order Gradient Plasticity Models

To consider the effects of the interactions and interplay among microstructures, gradient-dependent models of second- and fourth-order are included in the widely used phenomenological Johnson-Cook model where the effects of strain-hardening, strain rate sensitivity, and thermal-softening are successfully described. The various parameters for 1006 steel, 4340 steel and S-7 tool steel are assigned. The distributions and evolutions of the local plastic shear strain and deformation in adiabatic shear band (ASB) are predicted. The calculated results of the second- and fourth-order gradient plasticity models are compared. S-7 tool steel possesses the steepest profile of local plastic shear strain in ASB, whereas 1006 steel has the least profile. The peak local plastic shear strain in ASB for S-7 tool steel is slightly higher than that for 4340 steel and is higher than that for 1006 steel. The extent of the nonlinear distribution of the local plastic shear deformation in ASB is more apparent for the S-7 tool steel, whereas it is the least apparent for 1006 steel. In fourth-order gradient plasticity model, the profile of the local plastic shear strain in the middle of ASB has a pronounced plateau whose width decreases with increasing average plastic shear strain, leading to a shrink of the portion of linear distribution of the profile of the local plastic shear deformation. When compared with the second-order gradient plasticity model, the fourth-order gradient plasticity model shows a lower peak local plastic shear strain in ASB and a higher magnitude of plastic shear deformation at the top or base of ASB, which is due to wider ASB. The present numerical results of the second- and fourth-order gradient plasticity models are consistent with the previous numerical and experimental results at least qualitatively.

Experimental quantification of the plastic blunting process for stage II fatigue crack growth in one-phase metallic materials

The plastic blunting process during stage II fatigue crack growth was studied in pure polycrystalline Ni to investigate effects of strain localization and inelastic behavior on the kinematics of crack advance. Correlations were obtained between strain fields ahead of a fatigue crack, crack advance per cycle and crack growth kinetics. Strain fields were quantified using a combination of in situ loading experiments, scanning electron microscopy and digital image correlation for 8 < Δ K < 20 MPa m 1/2 and a fixed load ratio of 0.1. Results indicate that strain localized along a dominant deformation band, which was usually crystallographic and carried mostly pure shear for large loads and was of mixed character for lower loads. Instances of double deformation bands were observed, with bands acting either in a simultaneous or alternating fashion. It was found that the area integral of the opening strain for values larger than a given threshold, an “integrated” strain, had a power-law relationship with Δ K, with the exponent approximately equal to the Paris exponent ( m). Therefore, the crack growth rate was proportional to the integrated strain. An analysis based on this correlation and the presence of dominant shear bands indicated that the integrated strain is related to the accumulated displacement in the band. This, in turn, is proportional to the product of the cyclic plastic zone radius and the average shear strain ahead of the tip, which represents a basic length scale for plastic blunting. Assumptions on the load dependence of these quantities, based on their observed spatial variation, allowed estimating m = 2 1 + 1 1 + n ′ , where n′ is the cyclic hardening exponent (0 < n′ < 1). This gives 3 < m < 4, which accounts for about 50% of the observed values of m between 1.5 and 6 for a wide variety of metallic materials.

Strain summation in finite element modelling of multipass hot rolling

The shear strain distributions in two pass forward–forward (FF) and forward–reverse (FR) rolling have been modelled using plane strain finite element models of individual passes and then summing the results from the individual passes. This method gives excellent agreement with the average shear strain, defined by the net shear angle, and with the distribution of shear strain through the thickness, measured from the distortion of mild steel pins inserted through the thickness of experimentally rolled type 316L stainless steel slabs. The spread in breadth of the experimental slabs has little effect on the shear strain distribution or on the net equivalent strain at any position in the rolled slabs. For a given total reduction, the shear strain for FF two pass rolling is less than that for a single pass and is reduced when a smaller first pass and larger second pass reduction is applied. For FR two pass rolling, the shear strain of the first pass is essentially removed for 30%+30% reductions, but not for 50%+50% reductions. For the experimental conditions studied, the recrystallisation kinetics and recrystallised grain size produced by annealing after FF and FR two pass rolling are satisfactorily correlated by the net equivalent strain, with no evidence of any effect of the different strain paths to achieve the same value of equivalent strain.

Properties of piezoelectric voltage considering the microscopic structure of wood cell walls

Abstract The combined effects of the grain-angle (θ) and the microfibril angle (MFA) on the piezoelectric voltage (P) are discussed for a wood specimen subjected to unidirectional stress. The fiber axis of the specimen investigated was not parallel to the loading direction. A theoretical discussion is provided concerning fundamental elastic equations that predict the elastic strain field in the crystalline cellulose microfibril (CMF). It was assumed that an ideal wood specimen could be represented by a multi-tracheid model consisting mainly of the middle layer of the secondary wall. Experimental results revealed that plots of the piezoelectric voltage (P) versus the grain angle (θ) show concave curves with a maximum at θ=45°, regardless of MFA in the specimen. A similar tendency was obtained for the relationship predicted between the average shear strain along the CMF and θ. The results indicate that generation of a shear strain in the CMF positively contributes to the piezoelectric effect in wood.

Effects of constitutive parameters on adiabatic shear localization for ductile metal based on JOHNSON-COOK and gradient plasticity models

By using the widely used JOHNSON-COOK model and the gradient-dependent plasticity to consider microstructural effect beyond the occurrence of shear strain localization, the distributions of local plastic shear strain and deformation in adiabatic shear band(ASB) were analyzed. The peak local plastic shear strain is proportional to the average plastic shear strain, while it is inversely proportional to the critical plastic shear strain corresponding to the peak flow shear stress. The relative plastic shear deformation between the top and base of ASB depends on the thickness of ASB and the average plastic shear strain. A parametric study was carried out to study the influence of constitutive parameters on shear strain localization. Higher values of static shear strength and work to heat conversion factor lead to lower critical plastic shear strain so that the shear localization is more apparent at the same average plastic shear strain. Higher values of strain-hardening exponent, strain rate sensitive coefficient, melting point, thermal capacity and mass density result in higher critical plastic shear strain, leading to less apparent shear localization at the same average plastic shear strain. The strain rate sensitive coefficient has a minor influence on the critical plastic shear strain, the distributions of local plastic shear strain and deformation in ASB. The effect of strain-hardening modulus on the critical plastic shear strain is not monotonous. When the maximum critical plastic shear strain is reached, the least apparent shear localization occurs.

Effect of Cu additions on the structural and mechanical properties of Sn–Zn alloy

Highly pure Sn, Zn, and Cu were used to get Sn–8.6 wt.% Zn and Sn–8.6 wt.% Zn–(0.5–2 wt.%) Cu alloys prepared by the normal cast technique. The ingot was homogenized then swaged into wire of 0.8 mm in diameter and sheets of 1.5 mm thick. From the analysis of X-rays diffraction patterns, for Sn, binary and tertiary (with 1 wt.% Cu) alloys the average crystallite size and lattice strain were calculated. The samples were subjected to different axial loads and a torsion stress applied simultaneously. The accompanying elongation measured was found to increase with increasing both the axial load and the average shear strain but decreased with increasing Cu content. The large crystallite size of Sn was reduced by adding Zn, but adding Cu increased the crystallite size of the binary alloy. The maximum strength was reached with 1 wt.% Cu, while 0.5 wt.% Cu caused no significant variation of strength.