Residual Strain Distribution Research Articles

Dependence of deformation-induced magnetic field on plastic deformation for SUS304 stainless steel

In this paper, the correlation between plastic deformation and the deformation-induced magnetic field was exper- imentally investigated for the SUS304 austenitic stainless steel. Test-pieces with different shapes were fabricated to produce different strain distribution. Various plastic tensile loads were imposed into the specimens to introduce plastic deformations of different levels. The residual strain distributions at the surfaces of the specimens were measured by an optical 2D strain measurement system during loading process while the distributions of the deformation-induced magnetic fields above the specimens were measured by using a fluxgate magnetometer after each loading cycle. The experimental results show that the amplitudes of the magnetic field have a clear and repeatable relationship with the maximum residual strains for all the specimens, and the relationship is independent of the strain distribution. Based on the experimental results, the mechanism of the deformation-induced magnetic field was discussed, and a NonDestructive Evaluation (NDE) method was proposed for the quantitative evaluation of plastic deformation in the SUS304 stainless steel.

Residual Stress of Gear Meshing under Shakedown Condition with Direct Analysis

A shakedown mathematical model of gear contact has been developed. A direct method is applied to solve the mathematical model. Local coordinates are constructed on different meshing points because curvature of gear profile is not constant. Distributions of residual stresses and strains are given base on variable curvature surface. The numerical approach consists of an operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains. The eigenstrains are determined using an incremental projection method. Contact stresses and contact residual stresses of meshing gear teeth with standard and modified profile are computed. The results show compressive residual stress can improve capacity of gear and operating life. This aspect may contribute to future developments in the understanding of gear durability.

Residual Strain Distribution around a Fatigue-Crack Tip Determined by Neutron Diffraction

An analysis of residual stress, one of the contributory factors to the crack tip driving force, is extremely important to probe the fatigue crack growth mechanism and to further develop the life prediction methodology. Since fatigue crack growth is governed by crack-tip plasticity and crack closure in the wake of the crack tip, the investigation of residual stain/stress field in both behind and in front of the crack tip is crucial. In the current work, a 304L stainless steel compact-tension specimen is pre-cracked under constant-amplitude cyclic loading. Neutron diffraction is employed to directly measure the three orthogonal residual strain fields with 1-mm spatial resolution as a function of distance from the crack tip. The mapping results show that the three orthogonal residual-strain distributions around the crack tip depend on the stress multiaxiality, not following a single Poisson relationship to each axis.

Pattern formation in fiber-reinforced tubular tissues: Folding and segmentation during epithelial growth

Constrained growth processes in living materials result in a complex distribution of residual strains, which in certain geometries may induce a bifurcation in the elastic stability. In this work, we investigate the combined effects of growth and material anisotropy in the epithelial pattern formation of tubular tissues. In order to represent the structural organization of most organs, we adopt a strain energy density which accounts for the presence of a nonlinear reinforcement made of cross-ply fibers distributed inside a ground matrix. Using a canonical transformation in mixed polar coordinates, we transform the nonlinear elastic boundary value problem into a variational formulation, performing a straightforward derivation of the Euler–Lagrange equations for perturbations in circumferential and longitudinal directions. The corresponding curves of marginal stability are obtained numerically: the results demonstrate that both the three-dimensional distribution of residual strains and the mechanical properties of fiber reinforcements within the tissue are fundamental to determine the emergence of a specific instability pattern. In particular, different proportions of axial and circumferential residual strains can model the epithelial formation of mucosal folds in the esophagus and of plicae circulares in the small intestine. The theoretical predictions are compared with morphological data for embryonic intestinal tissues, suggesting that the volumetric growth of the epithelium can also drive the early stages of villi morphogenesis.

Feasibility study on a neutron diffraction method for non-destructive evaluation of residual strain distribution of a combustion chamber

A regeneratively cooled combustion chamber of a cryogenic liquid rocket engine is exposed to a large temperature difference between a combustion gas and a liquid hydrogen coolant. The large temperature difference induces large thermal stress in the chamber wall, and the strain is accumulated throughout the cyclic firing tests. Evaluation of the stress and the strain distribution in a chamber wall is essential for chamber life prediction because the chamber life is related to such stress and strain. A feasibility study on a neutron diffraction method for evaluation of residual strain distribution in a chamber wall was conducted. A method of positioning cooling channels inside a combustion chamber was established. The measurement time was adjusted to improve the fluctuation of the diffraction data. The measured data were compared with the numerical data by finite element analysis.

Analysis of Residual Strain and Stress Distributions in High Speed Milled Specimens using an Indentation Method

Analysis of Residual Strain and Stress Distributions in High Speed Milled Specimens using an Indentation Method

Contact Pressure and Residual Strain in 3D Elasto-Plastic Rolling Contact for a Circular or Elliptical Point Contact

What is often referred to as a Hertzian contact can undergo plasticity either at the macroscale, due to an accidental overload, or at an asperity scale, due to the presence of surface defects and/or roughness. An elastic solution does not explicitly consider the surface velocity or loading history, but it is also apparent that a moving (rolling) load will not yield the same residual stress and strain distribution as a purely vertical loading/unloading. Three-dimensional (3D) analysis is also more complex than the two-dimensional (2D) problem because it implies a change in the surface conformity. This paper presents the results of a numerical investigation of frictionless elastic-plastic elliptical point contacts with a moving load, as compared to a purely vertical (indentation) load. In the present analysis, both bodies may behave in an elastic-plastic mode. Both kinematic and isotropic hardening are considered to account for repeated rolling contacts. The contact pressure and the plastic strain are found to be reduced when the two bodies are elastic-plastic, as compared to the case in which one of the bodies remains elastic. Numerical results also indicate that at a given load intensity, the maximum contact pressure and equivalent plastic strain are affected by the contact geometry (circular and elliptical point contacts) and differ significantly when the load is moving as compared to purely vertical indentation. Although the maximum elastic contact pressure (Hertz solution) is often used as a control parameter for rolling contact fatigue analysis, whatever the geometry of the contact (point, elliptical, or line contact), the results presented here show that the effective contact pressure and subsequent residual strains are strongly dependent on the contact geometry in the elastic-plastic regime.

Reconstruction of axisymmetric strain distributions via neutron strain tomography

Predicting the behaviour of structural components under a particular set of loading conditions requires knowledge of the residual elastic strain distribution throughout the bulk of these components. Characterising the 3D strain state at any particular point involves the measurement of six independent components which make up the second order strain tensor. Mapping the complete strain distribution throughout large volumes thus presents significant practical challenges. One possible solution to this problem is to reconstruct the 3D variation of strain components using tomographic techniques. The basic principle underpinning this idea is that the multi-component strain tensor can be reconstructed from a redundant set of lower order projection data. Here we demonstrate this fundamental concept for two samples: a shrink fit ‘ring-and-plug’ sample, and a spray-quenched circular cylinder, both possessing axially symmetric internal strain distribution. We present and contrast different approaches to the strain tomography problem. The methods described here can also be readily applied to high-energy X-ray diffraction measurements and represent an important step toward developing the tomographic reconstruction framework for strain tensor distributions of arbitrary complexity. The major benefit of neutron strain tomography is that the incident beam flux is utilised more fully, greatly reducing the data collection times. Using micro-channel plate (MCP) neutron detectors, a spatial resolution of the order of 0.1 mm can be achieved [1].

Strain monitoring of a single-lap joint with embedded fiber-optic distributed sensors

We have developed a fiber-optic distributed sensor which can measure strain distributions along fiber Bragg grating (FBG) with the high spatial resolution. This sensing system is based on optical frequency domain reflectometry and a long-length FBG whose length is about 100 mm can be used. We can identify the longitudinal strain at an arbitrary position along the FBG using signal processing technology. In this study, long-length FBGs were embedded into the adhesive layers of the two single-lap joints and we could successfully measure the strain distributions inside the adhesives. In one single-lap joint, the adherends were carbon fiber reinforced plastics and in another one, they were aluminum. Theadhesive was epoxy in both cases. The measured results were compared with the calculated ones by nonlinear finite element (FE) analysis in which the large displacement and the elasto–plastic response of the adherend or adhesive material were account for. We found that in most of the applied loads, the agreement between the measured results and the calculated ones obtained from an intact FE model is excellent. While the measured strain distributions inside the adhesive layer of the aluminum single-lap joint were varied at the end of the overlap in the higher applied loads and they were much different from those of the intact model, an FE model with debonding was made and it could represent such variations. We could also monitor the strain distributions inside the adhesive during the manufacturing process and we observed the perturbation in residual strain distributions after curing. Consequently, we can say that the fiber-optic distributed sensor with the high spatial resolution is very useful not only to assess the structural integrity of adhesive joints but also to improve numerical analysis techniques and manufacturing processes for them.

Characterization of the residual strains in iterative laser forming

In laser forming, thermally induced strains transverse to the laser scan line vary with depth in the material and contribute most significantly to the desired deformation. The through-thickness transverse residual strain distribution was measured by neutron diffraction in laser-formed low carbon steel and aluminium alloy specimens. The specimens were formed with a wide range of laser line energies covering the temperature gradient mechanism (TGM) and shortening or upsetting mechanism (SM), and for single and multi-pass forming (up to 3 laser passes). Below the saturation line energy where the TGM dominates, the gradient of the through-thickness strain distribution was found to increase with increasing line energy and number of laser passes; the gradient decreased again at line energies above the saturation line energy where the efficiency of the TGM decreases. Iterative laser forming can be applied to reduce weld-induced distortions. The peak longitudinal strain measured in the weld seam of a specimen that had been straightened by iterative laser forming was also significantly reduced.

The Analysis of Gear Contact under Cyclical Load

Shakedown analysis of gear contact is very important. Local coordinates are constructed on different meshing points because curvature of gear profile is not constant and then distributions of residual stresses and strains are given. Upper and lower bounds for the shakedown limits have been obtained. The steady-state residual stresses of gear under repeat meshing are calculated and relations between shakedown limits and frictional coefficient/meshing position are given. The results are useful information for the strength design of gear.

Numerical Investigation on Heat Transfer and Residual Stress in a Butt Welded Plate

It is a well known fact that during welding, the metal at the welding zone gets melted and then solidifies, which results in shrinkage in all directions. Residual strain and stress distributions coming from shrinking are largely influenced by the nature and configuration of the welding process, metallurgical characteristics of weld, and the geometrical shape of the weld joint. The residual stress mainly depends on the thermal history cycle through which the specimen undergoes in the welding process. So these thermal history cycles are to be known in order to get a better knowledge of the welding phenomenon and to minimize the risk of failures. In this work, a detailed analysis has been carried out for predicting the heat flow pattern and stress distribution in an aluminum alloy plate during welding. In this study, the modified double ellipsoidal heat source distribution pattern is modeled and considered for the weld pool design. Elastic-plastic material properties at various temperatures are also considered for simulation. A detailed finite element analysis is carried out to predict the welding residual stress. In this, thermal analysis is carried out for actual variable welding speed and these transient thermal histories at various locations were numerically predicted and compared with experimental results. Further, these thermal results are used to predict the residual stress on the weld plate using finite element method.

Indentation behavior of functionally graded Al–SiC metal matrix composites with random particle dispersion

This study addresses the effects of number of layers, compositional gradient exponent (material composition) and random particle dispersion on the indentation behavior of a functionally graded metal matrix composite. The ceramic particles in a certain volume fraction were randomly distributed within each layer depending on the compositional gradient exponent in order to have a similar structure to an actual microstructure as possible. Increasing the number of layers caused an evident increase in indentation depths for all compositional gradient exponents. The compositional gradient exponent had an important effect on the indentation depth. The random particle dispersion also played an important role on the central indentation depth ( n < 3) as well as on the deformed surface profiles for both high layer numbers ( N = 75 and 150 layers) and the material compositions approaching to a metal-rich structure resulted in some fluctuations in the deformed surface profiles. Increasing the number of layers at a certain compositional gradient exponent resulted in larger mean residual stresses and plastic deformations. Increasing the compositional gradient exponent at a certain layer number decreased mean residual stresses and strains since the ceramic volume fraction is increased. The random particle dispersion also resulted in non-uniform residual stress and strain levels and distributions.

Residual plastic strain recovery driven by grain boundary diffusion in nanocrystalline thin films

Residual strain in metals is typically considered to be irreversible. However, residual strain in nanocrystalline materials can be recovered over a period of time via diffusive mechanisms. In this study, free-standing copper films of submicron thickness with an average grain size of about 40 nm are mechanically loaded via a plane-strain bulge test, and residual strain recovery at room temperature is characterized after unloading. The specimens recover their residual strain in a period of time that can range from a few days to more than 1 month depending upon the surface conditions and heterogeneous residual strain distributions in multiple cycles of recoveries. A constant tensile stress of about 25 MPa is reached after each recovery finishes. Two characteristic strain rates occur during residual strain recovery, a transient strain recovery rate of the order of 10 −7 s −1 and a steady-state strain recovery rate of the order of 10 −9 s −1. A model of the plastic strain recovery is presented which demonstrates the plausibility that grain boundary diffusion driven by chemical potential gradients due to residual stresses and the presence of voids can rationalize the transient and steady-state plastic strain recovery rates, respectively.

Non destructive neutron diffraction measurements of cavities, inhomogeneities, and residual strain in bronzes of Ghiberti’s relief from the Gates of Paradise

Quantitative neutron studies of cultural heritage objects provide access to microscopic, mesoscopic, and macroscopic structures in a nondestructive manner. In this paper we present a neutron diffraction investigation of a Ghiberti Renaissance gilded bronze relief devoted to the measurement of cavities and inhomogeneities in the bulk of the sample, along with the bulk phase composition and residual strain distribution. The quantitative measurements allowed the determination of the re-melting parts extension, as well as improving current knowledge about the manufacturing process. The study provides significant and unique information to conservators and restorators about the history of the relief.

Residual Stress, Texture, and Phase Investigation of Autogenous Edge Welds Using High Energy Synchrotron Radiation

Two autogenously edge welded beams made from SA508 ferritic steel were investigated with the purpose of validating residual stress modelling tools which are relevant for integrity assessment of structural power plant components. The two specimens were welded with two different torch travel speeds. The residual strain and phase distributions were non-destructively determined by high-energy synchrotron X-ray diffraction. Good agreement between numerical and experimental data was found for the specimen welded at fast speed. Furthermore, the texture changes in the specimen welded at slow speed were analysed by the same experimental technique.

Fully Two-Dimensional Discrete Inverse Eigenstrain Analysis of Residual Stresses in a Railway Rail Head

The aim of the present study was to introduce a new algorithm for reconstructing the eigenstrain fields in engineering components. A 2D discrete inverse eigenstrain study of residual stresses was carried out on a worn railhead sample. Its residual elastic strain distribution was obtained by neutron diffraction measurement in Stress-Spec, FRMII and used as the input for eigenstrain reconstruction. A new eigenstrain base function-tent was introduced to capture the fully two-dimensional variation of eigenstrain distribution. An automated sequential tent generation scheme was programed in ABAQUS™ with its preprocessor to load the experimental data and postprocessor to carry out the optimization to obtain the eigenstrain coefficients. The reconstructed eigenstrain field incurs residual stress distribution in the railhead simulation, which showed good agreement with the experimental data.

Experimental study on elasto‐optic effect in bulk GaN crystal

AbstractElasto‐optic effect has been studied experimentally in bulk α‐GaN crystal. By using an imaging type transmission polariscope, two‐dimensional distribution of refractive index difference |Δn | was measured in the c‐plane of beam‐like samples (3×3×10 mm3) while applying the external stress compressive to its longitudinal directions. The two‐dimensional distribution of |Δn | revealed its local fluctuation reflecting residual strain distribution of the sample because there is no natural birefringence in c‐plane. At the initial stage of stress impression, the |Δn | was increased or decreased at each point according to whether the residual strain is compressive or tensile along the stress‐applied direction. The |Δn | was finally increased with a similar slope at the final stress‐impression stage, regardless of the residual strain level. The |p11‐p12| was obtained as 0.13 from the averaged slope of the final stress‐impression stage, which is useful for estimating the magnitude of residual strain in c‐plane GaN substrates. (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Residual strain distribution in casting ingot of multi-crystalline silicon

Abstract By using a scanning infrared polariscope (SIRP), the residual strain distribution has been characterized in specially-prepared vertical slices of rectangular blocks cut from two conventional casting ingots in production scale. All the blocks clearly revealed local strain increase in the shapes of straight-pillar and long-pyramid but its distribution was significantly different from block to block. The averaged vertical profiles exhibited common W-shape in the center blocks, while it was more distorted in the peripheral blocks, which may reflect casting process condition such as thermal stress applied to the whole ingot.

A method for characterising residual strains around femtosecond laser microexploded waveguide by nanoindentation

In this paper, quartz wafer was microexploded by a commercial Ti: Sapphire regenerative amplifier (spectra physics, spitfire). And nanomechanical properties of the surface area that just above the laser induced waveguide were measured by a commercial nanomechanical test system (nano indenter XP, MTS Inc.). Indentation depth dependent changes in hardness can be found from nanoindentation experiments, which reflected the variations in plastic residual strains. Using the formula brought out in our previous work that correlate residual strains with hardness values measured by nanoindentation, the indentation depth dependent distribution of plastic residual strains in the area above femtosecond laser microexploded optical waveguide was explored. The mean plastic residual strains decreased from 0.048 to 0.01 in the indentation depth of 200 nm~700 nm, and kept to be 0.01 when the indentation depth was larger than 700 nm.