Elastic Strain Components Research Articles

Novel bulk triaxial residual stress mapping in an additive manufactured bridge sample by coupling energy dispersive X-ray diffraction and contour method measurements

A novel approach for determining triaxial residual stress states by coupling energy dispersive X-ray diffraction and contour method measurements is provided and validated in a Ti‐5Al‐5V‐5Mo‐3Cr additive manufactured (AM) bridge sample. Synchrotron X-ray diffraction (SXRD) can provide relatively fine spatial resolution (on the order of 10–100 µm) for mapping 3D elastic strain fields within a sample. However, for samples with dimensions larger than one or two centimeters the path length can get prohibitive as both constant wavelength and energy dispersive SXRD are based upon transmission measurements. As an example, for a plate-like sample geometry where the thickness is limited (less than a centimeter) it is trivial to measure the longitudinal and height direction elastic strain components with excellent in-plane spatial resolution (∼100 µm) and a somewhat lower through-thickness resolution (10–15 times larger) but obtaining the through thickness component is often not possible as the beam path must be parallel to one of the large dimensions of the plate. While small samples of low Z-number alloys (e.g., Ti or Al) allow determination of the three elastic strain components, this is often not the case for higher Z alloys (e.g., Fe or Ni) or large samples where some strain components can be indeterminable. To overcome these limitations, this work applies a combination of synchrotron X-ray diffraction and the contour method (a mechanical relaxation technique), to determine the triaxial stress state. This novel combination is demonstrated and validated in a relatively small additive manufactured sample where all three orthogonal strain components are accessible via X-ray diffraction for stress determination. The paper also explores methods for determining the strain-free lattice parameter, typically obtained from a small stress-free reference sample. This work shows that a small size AM sample is not stress free, producing unreliable magnitudes of strain and stress. Instead, a strain-free lattice parameter is determined using residual stress equilibrium conditions, which gives consistent strain and stress trends for both X-ray diffraction (alone) and the new diffraction-contour coupling technique. This demonstrates that the coupling technique can be confidently applied to samples to determine stress when path length (size or Z-number) prohibit determination of three orthogonal strain components via diffraction.

Undrained Cyclic Loading Response of Subgrade Soil Subjected to Varying Moisture Content and Stress Level

Subgrades that are constructed from fine-grained cohesive soils undergo large settlements; therefore, the study of their deformation behavior is important to avoid early deterioration in the traffic infrastructure. In this study, the deformation behavior of two different types of cohesive subgrade soils at different compaction states has been addressed that considered the effect of influencing factors, such as water content, deviatoric stress, and confining pressure (σ3). The results from the unconsolidated undrained cyclic triaxial tests show that the deformation behavior of soil is highly influenced by the level of applied deviatoric stresses and moisture content on the wet side of optimum (WS) and is slightly affected by σ3 and moisture content on the dry side of optimum (DS). The elastic strain (ɛe) component showed a decreasing trend with an increase in the number of load cycles (N) and then attained a steady value toward a higher N; however, the plastic strain (ɛp) component continuously increased for a given magnitude of applied cyclic deviatoric stresses (σd,c). From the test results, logarithmic strain models were proposed to predict the long-term total (ɛt) strain and ɛp that developed in cohesive subgrade soils, which were subjected to various combinations of variations in moisture content and stresses. The proposed model has been compared with the existing model and shows better prediction ability with a coefficient of correlation (R2) of >95% in most cases.

The elastic component of anisotropic strain dominates the observed shift in the F2g Raman mode of anelastic ceria thin films.

Raman spectroscopy is applied for non-destructive characterization of strain in crystalline thin films. The analysis makes use of the numerical value of the mode Grüneisen parameter γ, which relates the fractional change in the frequency of a Raman-active vibrational mode and the strain-induced fractional change in the unit cell volume. When in-plane, compressive biaxial strain in aliovalent doped CeO2-films is relieved by partial substrate removal, the films exhibit values of γ for the F2g vibrational mode which are ∼30% of the literature values for bulk ceramics under isostatic stress. This discrepancy has been attributed to a negative contribution from the anelastic (time-dependent) mechanical properties of aliovalent-doped ceria. Here we propose a way to "separate" anelastic and elastic contributions to the F2g mode Grüneisen parameter. Mechanically elastic yttria (Y2O3) films on Ti/SiO2/Si substrate serve as "control". The values of γ calculated from the change in frequency of the ∼375 cm-1 F2g Raman-active mode are close to the literature values for bulk yttria under isostatic stress. This work should serve to provide a protocol for characterization of selective sensitivity to different strain components of doped ceria thin films.

English translation of Giesekus's famous article on the elasticity of liquids

Starting from a suspension of elastic dumbbells or chain-like particle aggregates as a simple model of a viscoelastic liquid, the rheological equation of state is inductively derived into which the concept of an “elastic strain component” (recoverable strain) is incorporated and can be understood as a nonlinear extension of the so-called “generalized Maxwell model.” Here, the liquid is characterized by a sequence of nested continua, each associated with an elasticity law. The consideration of the directional dependence of the mobility of the structural elements requires that the behavior of the liquids represented in this way generally deviates from a Weissenberg liquid.

Complex unloading behavior of titanium alloy in cold and thermal-mechanical working

Unloading behavior is of crucial importance in metal forming, which particularly creates challenges for springback analysis and control of shape and dimensional accuracies of the manufactured components. For the working with hard-to-form materials at elevated temperatures, the thermal-mechanical coupling effect makes the unloading process more complicated and thus more difficult to model and control. Establishing an insight into the thermal-mechanical unloading behavior is crucial for ultimately improving the shape and dimensional accuracy of formed components. In this research, by using a near-alpha high-strength titanium alloy as a case study material, a series of continuous loading-unloading-reloading experiments within cold and warm forming domains were designed and conducted. Through the experiments, the complex unloading behavior, specially for the temperature-dependent degradation effect of elastic modulus and nonlinear stress-strain response, was investigated. A physically-based model was developed to reproduce the temperature-dependent nonlinear reduction effect of elastic modulus. In this model, the reversible mobile dislocation density is particularly included and represented to describe the evolving nonlinear elastic strain component upon unloading affected by both plastic strain and deformation temperature. Based on the model-based analysis, the mechanism accounting for the complex unloading nonlinearity in thermal-mechanical working was discussed and revealed from different evolutions of dislocation behaviors depending on plastic deformation and temperature.

Implementation and validation of true material constitutive model for accurate modeling of thick-walled cylinder swage autofrettage

The fatigue life prediction and associated fail-safe design of autofrettaged tubes require accurate stress modeling of each specific high-strength thick-walled cylinder during and after the autofrettage process, which depends largely on the elastoplastic behavior of the original steel tubes. However, the complex material behavior is dominated by the Bauschinger effect. Modeling swage autofrettage of such steel tubes remains problematic. This is a crucial issue that has not been resolved by any available modeling software. Therefore, the modeling and design of the autofrettage process for current and future materials depends upon extending the capability of current software.This research aims to develop a user-programmable function (UPF), USERMAT, to realize a user-defined material model that features true material constitutive behavior with the corresponding algorithms for accurate stress analysis of high strength thick-walled cylinders during the autofrettage process. The material constitutive model to be implemented can be formulated with high accuracy via an available material characterization, which can adapt to both nonlinear and linear strain hardening during the initial tensile loading, while the elastic modulus can be reduced during reversed-loading. It also incorporates the Bauschinger effect as a function of the prior tensile plastic strain during the nonlinear compressive reversed-loading phase and fits the experimental data of the true material model. Swage autofrettaged thick-walled cylinder case studies were reported. The results for residual radial and hoop stress and for elastic strain components were compared with independent, available neutron diffraction measurements, and they are in good agreement. Developing and integrating such a UPF into a standard finite element analysis software package is potentially the most significant unsolved fundamental modeling issue relating to re-yielding, fracture and fatigue of modern autofrettaged cylinders and pressure vessels. It can not only provide a fundamental understanding of the deformation mechanism and stress development within the high strength steel tubes during the autofrettage process, but also provide guidance for the design and optimization of the autofrettage manufacturing processes and of material selection for high intensity pressure vessels, a potential market of billions of dollars.

Combined experimental–numerical study on residual stresses induced by a single impact as elementary process of mechanical peening

AbstractPeening processes can be used as a fatigue enhancement treatment for metallic structures by locally introducing compressive residual stresses. A combined experimental–numerical study on a single‐impact process with a drop tower on the aluminium alloy AA5754, representing the elementary process of mechanical peening, has been performed to investigate different impact parameters on the residual stress profile. Residual stresses have been measured using high‐energy X‐Ray diffraction. A three‐dimensional finite element model is used to predict the residual stresses numerically. The elastic strain components from the numerical results are used to calculate residual stresses by assuming either a plane stress or a plane strain state for different specimen thickness to assess the validity of respective assumption. The validity of the numerical simulation is evaluated based on comparisons of the elastic strain profiles and the percentage loss in kinetic energy of the steel ball due to the impact for four different energies, showing overall a good agreement in the experimental–numerical comparisons.

Mathematical Modeling on the Residual Stresses in Coatings Due to Heat Treatments

Coatings are implemented on engineering metals and alloys to augment the surface properties such as hardness as well as resistance to wear and corrosion. Heat treatments of coated metals/alloys are performed to aid in the progress of the bonding of the coatings to the substrate. During the air cooling process, the difference in the compositions of the coating and the substrate materials causes them to cool at different rates, which leads to straining in them. The paper presents the research on the mathematical investigation to evaluate the residual stresses in coatings caused due to heat treatments and subsequent air cooling. The mathematical modelling is executed to formulate the equations to represent the residual stresses retained in the coatings due to the heat treatments and subsequent air cooling. Air cooling undergoes two stages namely the initial quenching phase and the final cooling phase. During the quenching phase, the strain was expressed by considering the elastic, plastic and thermal strain components. Poisson’s ratio, deviatoric stress differential of the modulus of plasticity, coefficient of thermal expansion and change in temperature are used to express the elastic, plastic and thermal strain components. During the final cooling phase, the strain was expressed by considering only the elastic and thermal stain components, as the plastic staining the coating material generally does not occur during the final cooling phase and occurs only during the initial quenching phase. From the strain components, the residual stresses for the coatings in the x, y and z axis were formulated. Thus, the total residual stress is the sum total of stresses caused during the initial quenching phase and the final cooling phase.

Effect of microstructural evolution on the cyclic softening of a 10% Cr martensitic steel under low cycle fatigue at 600 °C

Microstructure evolution and softening during interrupted low cycle fatigue (LCF) tests at 600 °C and constant strain amplitudes of ±0.2% and ±0.6% corresponding to dominance of the elastic and plastic strain components, respectively, was examined in a 10% Cr steel. Cyclic softening attributed to changes in the strengthening from dislocations and lath structure is more pronounced during the first half-life. The Burgers vector analysis of dislocation reveals the role of the single and multiple dislocation slip in retention and transformation of lath structure at cycling with low and high strain amplitude, respectively.

Effect of strain rate on fatigue property of A356 aluminium casting alloys containing pre-existing micro-voids

This study aims to investigate the dependence of fatigue life on strain rate variations by loading frequency, and simultaneously, to evaluate the mutual relation between the strain rate and microporosity on the fatigue property in terms of the defect susceptibility of fatigue life to microporosity variation. The test specimen was prepared from the rim section of an automotive wheel fabricated by low-pressure die-casting on an A356 alloy. The high-cycle fatigue test was carried out in a strain rate range corresponding to the frequency range of 0.3–30 Hz at a stress ratio of R = −1. The strain rate increased to a two-order interval from 10−2 to 100 s−1 as the loading frequency increased from 0.3 Hz to 30 Hz. The nominal fatigue strength coefficient and exponent decreased from 754 MPa and 0.18 to 293 MPa and 0.09, respectively, with increasing strain rate. The fatigue life in low-stress amplitude slightly increased with the strain rate, while it remarkably decreased with the strain rate as the stress amplitude increased. This is because the elastic/plastic strain component ratio (Δεe/Δεp) decreased upon increasing the plastic strain component, accompanied by increasing strain rate. The plastic strain component was remarkably increased with the strain rate and stress amplitude, and decreased by the strain-hardening effect on the lapse of fatigue cycle, even though the elastic strain component remained at a constant level, depending mainly upon the stress amplitude. Additionally, the contribution of microporosity to the variation of fatigue life was underestimated as the strain rate increased, and became more sensitive with the variation of the elastic/plastic strain component in the fatigue cycle as the stress amplitude increased. The main propagation path of fatigue cracks is changed from a mixed mode of the cracking failure by the damage evolution of eutectic Si particle and the matrix penetration by shear deformation of matrix region, to a cracking failure mode where the damage evolution of eutectic Si particles dominated as the strain rate increased.

The mechanical response of Hysol 4183 under constant strain rate loading and creep

A comprehensive mechanical characterization of a polymer named Hysol 4183 subjected to either constant nominal strain rate loading or creep was carried out. The constant nominal strain rate tests included uniaxial loading in compression and tension, and (confined) triaxial loading by using the sleeve method. The creep tests included compressive uniaxial creep and creep-recovery loading at different stress levels and triaxial (confined) creep using the sleeve method. All the experiments were conducted at constant room temperature. A strong dependency of the polymer’s mechanical properties upon the loading rate was observed. Likewise, differences were observed in the tension and compression regime. The confining pressure improves the mechanical resistance of the polymer in terms of strength, failure strain, and elastic modulus relative to uniaxial constant strain rate loading. Curve fitting is applied to the results to model both the constant strain rate, including the influence of the confining pressure, and uniaxial creep loading tests. The creep equations incorporate the elastic, viscoelastic, and viscoplastic strain components. The results predicted by the models are satisfactorily correlated with the measured experimental results.

Effect of retained austenite stability on cyclic deformation behavior of low‐alloy transformation‐induced plasticity steels

AbstractThe retained austenite (RA) characteristics of Al‐containing TRIP700 steels have been manipulated using varying bainitic isothermal transformation (BIT) processing. The microstructural evolution was investigated using optical microscopy and quantitative image analysis, while the amount of transformed RA was evaluated with the saturation magnetization (SM) technique. Cyclic behavior is found to depend on the applied strain amplitude and stability of RA. At strain amplitudes with comparable elastic and plastic strain components, cyclic softening prevails, facilitated by more stable RA microstructures and Low Cycle Fatigue (LCF) performance benefits from a lower RA stability, which controls the amount of cyclic softening rate. With increasing plastic strain component, a transition to cyclic hardening is observed, and the transition strain increases with increasing RA stability. LCF performance deteriorates because of excessive cyclic strain hardening promoting martensitic transformation. The effect is accompanied by a transition from mixed dimple/cleavage to cleavage‐type fracture characteristics.

Effects of residual stresses and localised strain-hardening on the fracture of ductile materials

The strain history of a ductile material can affect its apparent initiation fracture toughness as well as its resistance to subsequent crack growth. Using neutron diffraction or synchrotron X-ray diffraction in conjunction with digital image correlation, it is possible to map both the total strain around the tip of a propagating crack, and the elastic strain component. Separating the elastic and irreversible strain components allows us to experimentally investigate the effects that residual stresses and prior strain-hardening have on crack propagation. This article presents the results of two experiments using these techniques. In the first experiment, it was shown that residual stresses in a 7xxx-series aluminium alloy affect not only the initiation of fracture but also fracture propagation. During crack propagation, residual stress relaxation occurs due to extension of the crack and plastic deformation in the region ahead of the crack tip. This affects the material’s apparent crack growth resistance in a non-linear manner and hence changes its fracture stability. In a second experiment, it was shown that the plastic zone ahead of a crack in a ductile material (in this case a ductile ferritic steel) can be modified by localised strain-hardening prior to fracture. Localised strain-hardening using an indentation tool was observed to cause small increases in the specimens’ peak load capacity and its energy absorption prior to the onset of unstable tearing. Using synchrotron diffraction, it was shown that is because hardening a region ahead of the crack tip causes stress redistribution to this region and away from the crack tip itself during fracture loading. These findings can inform how ductile and semi-ductile fracture is treated in structural integrity assessment procedures, particularly in the presence of residual stress. They also suggest that new localised peening treatments to improve the fracture resistance of structures in certain areas may be possible.

On elastic deformations and decomposition of strain in granular media

The origin of global deformations in granular media stems from various concurrent mechanisms at the microscopic scale. Recent micromechanical studies have pointed out inadequacies of traditional elasto-plastic theories with elastic nucleus to describe such materials. In addition, the fundamentals of additive decomposition of global strain into mechanism-specific contributions have been questioned from a multiscale point of view due to appearance of emergent nonlinearities in the global response. The current study addresses the decomposability of strain and the existence of an elastic zone by systematically scrutinizing the energy aspects of granular deformation under quasi-static loading regime. The results show that the assumption of an exclusively elastic nucleus can potentially introduce non-negligible errors, even at strain ranges below 10−4. By relaxing commonly used assumptions which are often restrictive, a new constitutive model for elastic deformations in granular materials is developed to capture material response as a function of microstructure of the granular assembly. After verification through comparisons with discrete element simulations, the model has been used to investigate the decomposability of strain. The results demonstrate that the elastic strain component can only be extracted through numerical simulations where the dissipative mechanisms are “artificially” prohibited, which relegates the strain decomposition to an abstract concept.

Neutron diffraction and neutron imaging residual strain measurements on offshore wind monopole weldments

Residual stress measurement is of fundamental interest in order to estimate the service life of engineering components and structures subjected to various loading conditions operating in different environments. Destructive and non-destructive techniques are used for the evaluation of residual stresses. Neutron diffraction, as a non-destructive technique, is widely used to measure the elastic strain component of a specific atomic plane from which residual stresses can be calculated. Neutron imaging is an alternative technique which enables residual stresses to be measured through strain mapping of the area of interest. In this study, neutron diffraction measurements were performed in conjunction with neutron imaging to evaluate residual strains in a compact tension, C(T), specimen extracted from a welded plate made of S355 structural steel. Neutron diffraction and imaging are two complementary techniques which have been employed in this work by performing measurements on the Engin-X and newly developed IMAT instruments, respectively, at the Rutherford Appleton Laboratory. Neutron diffraction residual strain measurements in all three directions were conducted within the Heat Affected Zone (HAZ) of the weld area whereas longitudinal residual strains were measured using the neutron imaging technique. A comparison of the neutron diffraction and neutron imaging preliminary results has shown that neutron imaging can provide acceptable measure of residual strains compared to those of obtained from neutron diffraction. The results have been discussed in terms of the possible sources of error encountered in each measurement technique and the accuracy of each technique against the other.

Property control by elastic strain engineering: Application to graphene

Various carbon nanostructures, including graphene, are of great interest nowadays for many applications. It has been shown that graphene has unique physical and mechanical properties and its properties can be controlled by the applied strain. The objective of the present paper is to describe several physical properties of graphene that can be controlled by means of elastic strain engineering. The space of in-plane elastic strain components is divided into regions with different structural configurations and physical properties of graphene. It is shown that a gap in the phonon density of states is observed when graphene is strained close to the appearance of ripples. Sound velocities of unstrained graphene do not depend on the propagation direction but application of strain, apart hydrostatic tension, makes graphene elastically anisotropic. The orientation, amplitude and wavelength of unidirectional ripples in graphene can be controlled by a change in the components of the applied strain.

Modeling of non-linear rheological behavior of hard rock using triaxial rheological experiment

This paper presents an extensive laboratory investigation of the non-linear rheological mechanical characteristics of hard rock under cyclic incremental loading and unloading. A data processing algorithm is proposed to analyze the experimental data, determine the instantaneous elastic and plastic strain components, visco-elastic and visco-plastic strain components from the total strain, and separate the visco-elastic and visco-plastic strain curves from the total creep strain curves. The elasto-viscoplastic rheological behavior of iherzolite specimens at various confining pressures is thoroughly studied using the obtained experimental data. Based on the data, a non-linear elasto-viscoplastic rheological model containing various deformation components is proposed, by connecting a Hooke body, a parallel combination of Hooke and plastic slide bodies, a Kelvin body, and a generalized Bingham body.The proportion of instantaneous plastic strain component in the total instantaneous strain has increasing tendency with higher deviatoric stress on a whole. The instantaneous elastic modulus of specimen tends to increase with higher deviatoric stress and confining pressure, the instantaneous plastic modulus of specimen is decreased with higher deviatoric stress at confining pressures of 3 and 6MPa on the whole, however, has no evident relationship with deviatoric stress, when confining pressure is increased to 9 and 16MPa. The proportion of the visco-plastic strain component in the creep strain is increased with higher deviatoric stress. The steady-state creep strain rate versus deviatoric stress relationship can be well described with an exponential expression. The elasto-viscoplastic characteristics of radial creep is similar to that of axial creep, but radial creep strain is only 25–30% of axial creep strain, steady-state creep rate in radial direction is about 35% of that in axial direction.

Numerical and experimental investigations of the anisotropic transformation strains during martensitic transformation in a low alloy Cr-Mo steel 42CrMo4

Abstract Hot forming as a coupled thermo-mechanical process comprises of numerous material phenomena with a corresponding impact on the material behavior during and after the forming process. Within the subsequent heat treatment, possible rapid cooling of the hot formed parts leads to the diffusionless decomposition of austenite into martensite. In this context, in addition to the elastic, plastic and linear thermal strain components, complex isotropic as well as anisotropic transformation strains can occur. Irreversible anisotropic transformation strains account for the plastic deformation at the phase boundary between the emerging and the parent phase and are related to the transformation induced plasticity (TRIP or TP) phenomena. Moreover, TRIP strains can be reduced or amplified by varying the current stress state. These phenomena significantly contribute to the final residual stress state and may be responsible for the cost-intensive component defects arising due to thermal shrinkage. This study aims at developing an FE-based material model in order to describe and quantitatively visualize stress dependence of the transformation induced anisotropic strains for a typical forging steel 42CrMo4. The developed material model as well as the aspects of its implementation in a commercial FE-system (Simufact.forming) is presented. Consequently, the discussed material model is tested by comparison of experimental and numerical results with respect to resulting dilatation under various stress states.

Research of consumer properties of leather filled with the use of electroactivated water reagent solutions

Consumer properties of the filled macroporous chrome­tanned semi­finished leather obtained by the developed technology using electrochemically activated aqueous solutions of the composition comprising xanthan acrylamide were studied. Sorption­desorption properties of different sections of the filled material during its interaction with water, relaxation and deformation characteristics, differential moisture content on a thermo­gravi­calorie­metric installation, volume yield were determined. It was found that the leather material obtained by the developed technology has higher elastic and plastic strain components by 1.7 and 1.3 times respectively compared with the current technology; porosity, volume yield and hygroscopic ability of obtained samples exceed those of the samples of the experimental technology by 4.5; 19.0; and 9.8–11.3 % respectively. The technology of filling of chrome­tanned leather material from pig skin is implemented by diffusion of the composition ingredients in the anolyte solution at pH 4.2–4.4 with the reduction of surface tension, the formation of mostly hydrogen bonds between the elements of the modified structure of collagen and the filler reagents. The interaction with water results in partial destruction of bonds that are restored after moisture removal. Optimum consumer properties are achieved at a certain ratio of the hydrophilic ability and the differential porosity type of the leather material. The use of the filling composition involving xanthan acrylamide in the anolyte provides effective alignment of porosity in different sections of the semi­finished product due to preferred filling of large pores and increase in the specific volume of smaller pores with the composition. The resulting fine­pored leather material with the split fibrillar structure causes a smaller loss of its area by 0.3 % after moisturizing and drying processes compared with the current technology. The leather material formed using the developed technology due to the complex of consumer properties is recommended for making the insides of shoes – insoles and lining and moisture removal material in the mechanical surface cleaning of products and structures.

Digital image correlation analysis of strain recovery in glassy polymer network isomers

Digital image correlation techniques were applied to compressive strain recovery experiments of glassy network isomers to study architectural contributions to deformational response. Strain recovery experiments provided a direct comparison of network isomer structure on viscoelastic deformation. Diglycidyl ether of bisphenol-A (DGEBA) was cured with 3,3′- and 4,4′-diaminodiphenyl sulfone (33DDS and 44DDS). The comparison revealed the networks have similar elastic and plastic strain components, but differ in anelastic strain response. DGEBA cured with 44DDS developed pre-yield anelastic strain at a significantly higher rate attributed to increase in free volume, molecular motions and energy dissipation. In contrast, DGEBA cured with 33DDS displayed lower pre-yield energy dissipation attributed to lower free volume and molecular motions, but exhibited a higher degree of post-yield strain-softening due to larger segmental rearrangements.