Cyclic Strain Paths Research Articles

Influences of cyclic stress paths on deformation behavior of saturated marine coral sand: An experimental study

The deformation of foundations in saturated marine coral sand induced by dynamic loading such as that from waves, earthquakes, tsunamis, and hurricanes is a key factor endangering the safety of marine engineering. However, the deformation characteristics of coral sand in the marine environment are complex and have rarely been studied. A number of undrained cyclic shear tests are performed with saturated coral sand under various consolidation conditions and cyclic stress paths. The results show that the medium-dense coral sand specimens exhibit two deformation failure modes: plastic strain accumulation and cyclic mobility. A novel method for cyclic strain path is presented to characterize the progressive development of cyclic deformation, and an important finding is that the difference between the cumulative plastic component and cyclic component at 5% deviator strain can be used to distinguish between the deformation failure modes. Another finding is that the parameter λ related to deviator strain rate and cyclic loading frequency can be used to distinguish the deformation failure modes. A relationship between complex stress conditions and deformation failure modes is established based on analyzing the major and minor principal stress. The proposed method provides new insights into the mechanics of deformation failures in saturated coral sand.

Comparisons on liquefaction behavior of saturated coral sand and quartz sand under principal stress rotation

A series of undrained cyclic axial-torsional shear tests on saturated coral sand and quartz sand under linear, circular, and heart stress paths are performed. The test results show significant differences in liquefaction characteristics for coral sand and quartz sand. A unique relationship between deviatoric strain amplitude and excess pore water pressure ratio (R u) can be established regardless of cyclic stress paths. The termed cyclic strain path is introduced to describe the generation features of strains, and different failure patterns for various cyclic stress paths can be easily identified. Moreover, the dissipative energy required to liquefaction triggering (E a1) of coral sand is much larger than that of quartz sand. The generation patterns of dissipative energy with R u for both sands are almost independent of cyclic stress paths, but the correlation between the cyclic stress ratio (CSR) and the number of cycles required to liquefaction triggering (N f) is dependent on cyclic stress paths. Using the proxy of the unit cyclic stress ratio (USR) proposed by Chen et al. (2020) instead of the CSR, the correlation between USR and N f is independent on cyclic stress paths. A remarkable finding is that, a unique correlation between USR15 and E a1 exists for all sands considered.

Surface Hardening of AlMg<sub>5</sub>Si<sub>2</sub>Mn Alloy through Multi-Axis Compression Using Max Strain

Severe plastic deformation (SPD) processing techniques are applied to polycrystalline metallic materials in order to refine the grain size up to the sub-micrometre or nanometer level. The decrease in grain size to a sub-micrometre level is related to beneficial mechanical properties such as very high strength. The most widely applied SPD method is equal-channel angular pressing (ECAP). In distinction to traditional cold rolling or drawing, SPD techniques frequently employ cyclic strain paths that can lead to an essentially unchanged shape of the material sample after processing. In this paper, multi-axis compression is applied by using the MAXStrain (R) unit to impose cyclic compression in two mutually orthogonal directions. This study is aimed to realize the evolution of microstructure and mechanical properties of AlMg5Si2Mn aluminium cast alloy subjected to multi-axis compression. The microstructure of the alloy in the as-cast and as deformed state was characterized by light and scanning electron microscopy. The results reveal that multi-axis compression has a great influence on the evolution of microstructure and final mechanical properties. The enhanced mechanical properties are associated with the progressive formation of refined microstructure which is heterogeneously distributed across the sample.

Experimental and numerical investigation of texture evolution and the effects of intragranular backstresses in aluminum alloys subjected to large strain cyclic deformation

Strain hardening in FCC metals and alloys can be accompanied by the formation of deformation induced dislocation microstructures. These microstructures tend to form dislocation cells or nets which are characterized by three-dimensional tangles of dislocations that serve as “cell walls” and less dense internal regions “cell interiors”. The presence of such dislocation microstructure induces intragranular backstresses due to blockage of dislocation passage leading to kinematic hardening at the macroscopic scale. The present work focuses on the effects of dislocation induced backstresses and the accompanying texture evolution on strain hardening behavior of AA 6063-T6 extruded aluminum alloy during cyclic forward-reverse-forward (FRF) simple shear deformation. The accompanying texture evolution is characterized using electron backscatter diffraction (EBSD) texture measurements. The development of the underlying dislocation substructure during the cyclic simple shear loading is determined using transmission electron microscopy (TEM). Furthermore, a new crystal plasticity backstress hardening model is proposed to incorporate the effects of intragranular backstresses due to the dislocation cells substructure. The hardening model is validated by comparing the numerically predicted results against the experimental cyclic simple shear flow response as well as texture evolution. An excellent agreement is found between the simulated and experimental results. In particular, the proposed model is able to predict the experimentally observed Bauschinger effect as well as the accompanying texture evolution during cyclic simple shear testing. The applicability of the proposed backstress hardening model is further validated by applying it to different cyclic strain paths (i.e. tension-compression-tension (TCT) and compression-tension-compression (CTC)) for different strain amplitudes. The numerically predicted results show good agreement to the corresponding experimental cyclic test results.

Biaxial cyclic plasticity experiments and application of a constitutive model for cyclically stable material behaviour

An extensive experimental program was conducted on AISI 4140 steel under cyclic proportional and non-proportional biaxial strain histories. The application of a plasticity model for cyclically stable material behaviour based on the idea of distance in stress space is described. A detailed explanation is provided of the methodology to derive from the experimental data the metric coefficients needed for calculating distances and the hardening modulus function required in the flow equations. The model gives accurate results for the cyclic stress–strain curves obtained in proportional strain tests. It also calculates correctly the stabilized stress values in 90° out-of-phase experiments. For more complicated non-proportional cyclic strain paths, the stresses calculated with the model reproduce strikingly well the qualitative evolution of the experimental response. The quantitative agreement is also good, but obviously not as good as for the simpler strain histories.

A constitutive model of twinning and detwinning for hexagonal close packed polycrystals

A new constitutive model to describe twinning and detwinning for polycrystalline materials with the hexagonal close packed (HCP) crystallographic structure is developed and implemented in the recently developed elastic viscoplastic self-consistent (EVPSC) polycrystal model. The new model is then applied to magnesium alloy Mg–3 Al–1 Zn (AZ31B) sheet under cyclic loadings and strain path changes. It is demonstrated that the new twinning model is able to capture key features associated with twinning and detwinning observed experimentally.

Research on the drawing process with a large total deformation wires of AZ31 alloy

Magnesium and their alloys have been extensively studied in recent years, not only because of their potential applications as light-weight engineering materials, but also owing to their biodegradability. Due to their hexagonal close-packed crystallographic structure, cold plastic processing of magnesium alloys is difficult. The preliminary researches carried out by the authors have indicated that the application of the KOBO method, based on the effect of cyclic strain path change, for the deformation of magnesium alloys, provides the possibility of obtaining a fine-grained structure material to be used for further cold plastic processing with large total deformation.The main purpose of this work is to present research findings concerning a detailed analysis of mechanical properties and changes occurring in the structure of AZ31 alloy wire during the multistage cold drawing process. The appropriate selection of drawing parameters and the application of multistep heat treatment operations enable the deformation of the AZ31 alloy in the cold drawing process with a total draft of about 90%.

Multiaxial cyclic deformation and non-proportional hardening employing discriminating load paths

Some novel discriminating multiaxial cyclic strain paths with incremental and random sequences were used to investigate cyclic deformation behavior of materials with low and high sensitivity to non-proportional loadings. Tubular specimens made of 1050 QT steel with no non-proportional hardening and 304L stainless steel with significant non-proportional hardening were used. 1050 QT steel was found to exhibit very similar behavior under various multiaxial loading paths, whereas significant effects of loading sequence were observed for 304L stainless steel. In-phase cycles with a random sequence of axial-torsion cycles on an equivalent strain circle were found to cause cyclic hardening levels similar to 90° out-of-phase loading of 304L stainless steel. In contrast, straining with a small increment of axial-torsion on an equivalent strain circle results in higher stress than for in-phase loading of 304L stainless steel, but the level of hardening is lower than for 90° out-of-phase loading. Tanaka’s non-proportionality parameter coupled with a Armstrong–Fredrick incremental plasticity model, and Kanazawa et al.’s empirical formulation as a representative of such empirical models were used to predict the stabilized stress response of the two materials under variable amplitude axial-torsion strain paths. Consistent results between experimental observations and predictions were obtained by employing the Tanaka’s non-proportionality parameter. In contrast, the empirical model resulted in significant over-prediction of stresses for 304L stainless steel.

Effect of reverse and cyclic shear on the work-hardening of AISI 430 stainless steel

Sheet metal forming commonly involves various processing steps leading to complex strain paths. The work hardening of the metal under these circumstances is different from that observed for monotonic straining. The effect of the strain path on the hardening of materials is usually studied through sequences of standard mechanical tests, and the shear test is especially well adapted to such studies in sheet forming. Shear straining covering Bauschinger and cyclic strain paths were used in the analysis of the hardening of AISI 430 stainless steel sheets. The tests were conducted at 0°RD, 45°RD, and 90°RD (Rolling Direction) and for three effective strain amplitudes. The results indicate that the material presents Bauschinger effects and strain hardening transients that are sensitive to the testing direction. In addition, the cyclic straining leads to an oscillating stress pattern for the forward and reverse shearing cycles, which depends on the deformation amplitude.

Microstructure and Texture of Mg-Based AZ Alloys after Heavy Deformation under Cyclic Strain Path Change Conditions

The effects associated with the change of the deformation path - such as the replacement of homogeneous multi-slip by heterogeneous deformation and a decrease of global strain hardening - have been utilised in the metal forming operation termed KOBO technology. In the case of extrusion it consists in reversible, cyclic twisting of a billet under the extrusion force. The technology enables extrusion of metals with very large deformation in one operation at low temperature. A complex scheme of straining, large cumulated deformation and low temperature of the process results in a fine grained microstructure of the extruded material (product). The new technology requires detailed studies of the mechanism of the plastic deformation with the specific geometry of the zone of metal flow during extrusion. Essential in these studies is the information on the texture and microstructure in the deformation zone. The aim of this work is therefore to disclose the deformation mechanisms on the basis of the observations of microstructure and texture evolution in the zone of plastic flow of the extrudate. Coarse grained polycrystalline billets of magnesium alloys AZ31 were extruded by KOBO at room temperature and also by a conventional method at about 400°C. Methods of texture topography as well as optical observations reveal the specific microstructure and texture in mezzo and micro scale of heavily deformed material after extrusion. It is worth mentioning that the KOBO process leads to compact and rather homogeneous extrudates even in the case of AZ alloys. These hexagonal metals cannot be cold-formed to a high reduction with conventional techniques.

Evolution of Microstrains at Cyclic Incremental Deformation of Steel 42CrMo4

X-ray diffraction line profiles of a ferritic-pearlitic steel at different stages of monotonic and cyclic incremental strain paths were recorded and peak broadening was regarded. Evaluation of integral peak widths shows, that the distortion of structure is strongly dependent on the deformation path. The results for peak broadening at different deformation states correlate with flow stress behaviour and can be explained with certain dislocation arrangements.

The asymptotic behavior of perfectly elastoplastic model under periodic square generalized strain paths

The perfectly elastoplastic model has been investigated previously under rectilinear generalized strain paths and cyclic circular strain paths. Being subsequent to these studies we subject the model to cyclic square generalized strain paths, for which the effects of nonproportionality of generalized strains and piecewise continuity of generalized strain rates can be investigated. It is found that the cyclic responses depend on the amplitude ratio and also on the initial generalized stress. The criterion of elastic shakedown is provided and the concept of elastic shakedown attractors is introduced. Then the behavior is classified in the space of initial generalized stresses. The boundaries of four elastic shakedown regions and elastic region are derived. It is only for larger values of amplitude ratio that the region IV appears. The formula used to estimate the closeness to the limit point is developed, and using that concept we derive a formula to evaluate the error induced when an asymptotic response is used to replace the exact one. For larger amplitude ratio the asymptotic response is almost identical to the exact response.

The effect of cyclic strain path on the properties and structure of CuAl10 aluminium bronze

The improvement of metals formability by proper control of temperature, strain rate, and strain has been rather exhausted. The other way to obtain this goal is proper control of strain path. In the case of sheet metals the effect of strain path is widely known, but in massive metal forming processes that phenomena have been just under investigations. In the paper the effects of different cyclic strain paths on the mechanical properties and structures of CuAl10 aluminium bronze have been described. The strain paths contain various cyclic torsions. The amplitude was changed in the range of 0.01–0.6, temperature from 20 to 650°C and strain rate from 0.01 to 1s−1. The properties and structures obtained in cyclic strain paths are compared with those gained in monotonic torsion. It has been found that the flow stress in minor cyclic torsion is substantially dependent on cyclic conditions, mainly the strain amplitude used. The strain paths similar to those applied in the investigations are observed in some industrial processes.

Hardening behavior of three metallic alloys under combined stresses at elevated temperature

Initial and subsequent yield loci for type 316 stainless steel, Haynes 188, and Inconel 718 are determined experimentally in the axial-shear stress plane at 650 ∘C. Each of these materials has a face centered cubic (fcc) crystal structure, but entirely different chemical compositions and strengthening mechanisms. Material hardening behavior is described along three cyclic strain paths having a maximum equivalent strain of 0.015 m/m: fully reversed axial (Path I), fully reversed shear (Path II), and a nonproportional hourglass shaped path (Path III). Yielding is defined by a Mises-type equivalent offset strain definition having a target value of 30 μm/m. These types of yield surface determination tests are difficult, but fairly common in lower temperature ranges where precision strain gages can be used. Due to the high temperature in this study, axial and shear strains were measured by an extensometer. These results, which describe material hardening by the evolution of size, shape, and position of the current yield surface can be used in support of constitutive models for high temperature metallic materials. Hardening behavior of all three alloys is well described by a mixed hardening rule comprised of isotropic, kinematic, and distortional components. Relative to published work at lower temperatures, the isotropic hardening component is larger and the distortional hardening component is smaller than anticipated.

Sand Drain Design Based On Cyclic Strain-Path Controlled Triaxial Data

Sand Drain Design Based On Cyclic Strain-Path Controlled Triaxial Data

The Endochronic Approach for Structural Steel Subjected to Cyclic Loading

ABSTRACTThe A36 structural steel shows significant Baushinger effect under cyclic loading. Present paper modifies the anisotropic endochronic model to describe the behaviors of the A36 structural steel subjected to cyclic loading. The deformation induced anisotropy has been considered to modify the definition of the intrinsic time. Also, the different hardening functions are used with respect to the mechanical behavior under loading and unloading condition, respectively. Then, the presented constitutive equations are used to describe the mechanical behaviors of the A36 structural steel under different cyclic strain paths. The theoretical results are compared with the experimental data. The test investigated includes several different cyclic uniaxial and axial-torsional loading experiments from Hong and his co-workers. It is shown that the present model is capable of describing the anisotropic behaviors of A36 structural steel well.

High-Resolution EBSD Analysis of Severely Deformed Submicron Grained Aluminum Alloys

AbstractThere is currently much interest in the use of severe plastic deformation techniques for the production of submicron grained Al-alloys. Because of their small grain sizes, previous investigations have relied on the TEM to study the grain structures after processing. However, the TEM is not that well suited to obtaining statistically significant data on the misorientations of the boundaries present in the deformed state. Recent improvements in the resolution of SEMEBSD systems means that this powerful technique can now be used to quantitatively analyse severely deformed structures more reliably than was previously possible. Results using this method have shown that the deformation structure is very sensitive to the strain path, material, and processing conditions. With a constant strain path fibrous grain structures tend to be formed and homogeneous submicron grain structures can only be produced at very high plastic strains, of greater than ten. Materials deformed with cyclic strain paths are more isotropic, but generally have bimodal grain structures and contain a lower density of high angle boundaries and only bands of submicron grains.

A nonclassical constitutive model for crystal plasticity and its application

A nonclassical constitutive description for a slip system is formulated by using a simple mechanical model consisting of a spring and a plastic dashpot-like block. The corresponding constitutive model for a single crystal and the analysis for polycrystalline response is proposed based on the KBW's self-consistent theory. The constitutive model contains no yield criterion, so the corresponding numerical analysis is greatly simplified because it involves no additional process to search for the activation of slip systems and slip direction. A mixed averaging approach is proposed to obtain the response of polycrystalline material, which consists of the Gaussian integral mean for the ω which varies continuously within each face of the isohedron and the arithmetic mean for the spatially uniformaly distributed twenty sets of 0 and ϕ determined by the normal of each face of the isosohedron. The main features 316 stainless steel subjected to typical biaxial nonproportional cyclic strain paths are well described. Calculation also shows that the developed model and the corresponding analytical approach are of good accuracy and efficiency.

DEVELOPMENT OF A CONSTITUTIVE MODEL FOR BIAXIAL LOW‐CYCLE FATIGUE

Abstract— A version of the endochronic theory of plasticity for the modelling of nonproportional cyclic loading has been developed. To describe an additional hardening of a material a new engineering method for defining a nonproportionality parameter is proposed for a wide class of cyclic strain paths with a prescribed maximum range of plastic or total strains. This parameter makes it possible to establish an unambiguous linear dependence between the cyclic strain path shape and the stress level in a stabilized state. Conjugation conditions have been formulated to describe complex histories of nonproportional cyclic loading. The results of the modelling are shown to be in fair agreement with the experimental data.

Nonproportional Low Cycle Fatigue Criterion for Type 304 Stainless Steel

This paper describes a multiaxial low cycle fatigue parameter for correlating Hues under nonproportional loadings. Constant amplitude low cycle fatigue tests were carried out under 14 proportional and complex nonproportional cyclic strain paths using type 304 stainless steel hollow cylinder specimens at room temperature. In nonproportional loading tests, fatigue lives are decreased by as much as a factor of 10 in comparison with those in proportional loading tests with the same strain range. Reduction in fatigue life due to nonproportional loading is closely related to additional nonproportional cyclic hardening. The product of the maximum principal stress and strain ranges correlated the nonproportional fatigue data. A nonproportional cyclic hardening parameter computed from the strain path is also proposed that allows life estimates to be obtained directly from the strain history without the need for a cyclic plasticity model.