Measurement and Prediction of Residual Stresses in Quenched Stainless Steel Components

Austenitic stainless steel cylinders and rings are spray water quenched to create residual stresses at or greater than the yield strength. The residual stresses are measured using neutron diffraction, and two mechanical strain relaxation methods: deep hole drilling and incremental centre hole drilling. This paper compares the measurements with predictions of quenching using finite element analysis. Also finite element analysis is used to mimic deep hole and incremental centre hole drilling methods and to reconstruct residual stresses as if they have been measured. The measurements reveal similar trends to the predictions but there is only limited agreement between their magnitudes. However, there is better agreement between the reconstructed stresses and the measurements. Both the two mechanical strain relaxation methods reveal that large discrepancies occur between measurements and predictions arise because of plasticity. Irrespective of this and surprisingly there is good agreement between deep hole drilling and neutron diffraction measurements.     

Mixed numerical–experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens

This paper presents a mixed numerical–experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials. A biaxial tensile test is performed on a cruciform test specimen. The heterogeneous displacement field is observed by a CCD camera and measured by a digital image correlation (DIC) technique. The measured displacement field and the subsequently computed strain field are compared with a finite element simulation of the same experiment. The four independent engineering constants are unknown parameters in the finite element model. Starting from an initial value, these parameters are updated till the computed strain field matches the experimental strain field. Two specimen geometries are used: one with a centered hole to increase the strain heterogeneity and one without a hole. It is found that the non-perforated specimen yields the most accurate results.     

爆炸荷载下青砂岩动态起裂韧度的测试方法

为了研究爆炸荷载下青砂岩I型裂纹动态断裂韧度的测试方法,利用内部中心单裂纹圆盘（internal center single crack disc,ICSCD）试样进行了爆炸试验研究。试样由外径为400 mm、内部加载孔径为40 mm、预制裂纹长为60 mm的青砂岩制成。利用同步触发器实现圆盘中心起爆,并同步触发超动态应变仪,通过径向应变片获取爆炸应变曲线、裂纹尖端的环向应变片获取裂纹起裂时刻。以实测爆炸应变曲线为参量,应用Laplace变换推导出试样加载孔壁应力时程曲线表达式,并用数值反演法得出其数值解。利用ANSYS有限元软件,建立数值计算模型,通过相互作用积分法得出了在爆炸荷载作用下砂岩的I型动态应力强度因子曲线。研究结果表明：（1）ICSCD试件能够很好地用来测试岩石的动态起裂韧度;（2）炮孔周边的应力可以通过拉普拉斯变换的数值反演方法得到;（3）通过试验-数值法能稳定计算出ICSCD砂岩构型的动态起裂韧度,其最大误差仅为7%。

     

Load-Inversion Device for the High Strain Rate Tensile Testing of Sheet Materials with Hopkinson Pressure Bars

A high strain rate tensile testing technique for sheet materials is presented which makes use of a split Hopkinson pressure bar system in conjunction with a load inversion device. With compressive loads applied to its boundaries, the load inversion device introduces tension into a sheet specimen. Two output bars are used to minimize the effect of bending waves on the output force measurement. A Digital Image Correlation (DIC) algorithm is used to determine the strain history in the specimen gage section based on high speed video imaging. Detailed finite element analysis of the experimental set-up is performed to validate the design of the load inversion device. It is shown that under the assumption of perfect alignment and slip-free attachment of the specimen, the measured stress–strain curve is free from spurious oscillations at a strain rate of 1,000 s^?1. Validation experiments are carried out using tensile specimens extracted from 1.4 thick TRIP780 steel sheets. The experimental results for uniaxial tension at strain rates ranging from 200 s^?1 to 1,000 s^?1 confirm the oscillation-free numerical results in an approximate manner. Dynamic tension experiments are also performed on notched specimens to illustrate the validity of the proposed experimental technique for characterizing the effect of strain rate on the onset of ductile fracture in sheet materials.     

Micromechanical modelling and simulation of chopped random fiber reinforced polymer composites with progressive debonding damage

The aim of the present paper is to provide a quantitative prediction of the elastic-damage behaviour of randomly oriented fiber polymer composites. A constitutive model based on micromechanical considerations is presented. The nucleation and growth of voids induced by progressive fiber debonding is combined with the constitutive relationship. Failure resulting of excessive damage accumulation is captured by a critical void volume criterion and a vanishing element technique. Experimentally, damage accumulation in random glass fiber–polyester composites was monitored by a videoextensometry technique able to control the local strain rate. Good agreement of model predictions with experimental data is pointed out. The model was implemented into a finite element program and numerical applications on composite structures (a tensile specimen and a plate containing a central hole) are presented to illustrate the capability of the approach. Digital image correlation method was also used to measure the full-field strain in a notched specimen under tensile loading. The simulated results compared favourably with those obtained from experiments.     

A reexamination of plasticity-induced crack closure in fatigue crack propagation

The crack closure concept is often used to consider the R-ratio and overload effects on fatigue crack growth. The presumption is that when the crack is closed, the external load produces negligible fatigue damage in the cracked component. The current investigation provides a reassessment of the frequently used concept with an emphasis on the plasticity-induced crack closure. A center cracked specimen made of 1070 steel was investigated. The specimen was subjected to plane-stress mode I loading. An elastic–plastic stress analysis was conducted for the cracked specimens using the finite element method. By applying the commonly used one-node-per-cycle debonding scheme for the crack closure simulations, it was shown that the predicted crack opening load did not stabilize when the extended crack was less than four times of the plastic zone size. The predicted opening load was strongly influenced by the plasticity model used. When the elastic–perfectly plastic (EPP) stress–strain relationship was used together with the kinematic hardening plasticity theory, the predicted crack opening load was found to be critically dependent on the element size of the finite element mesh model. For R = 0, the predicted crack opening load was greatly reduced when the finite element size became very fine. The kinematic hardening rule with the bilinear (BL) stress–strain relationship predicted crack closure with less dependence on the element size. When a recently developed cyclic plasticity model was used, the element size effect on the predicted crack opening level was insignificant. While crack closure may occur, it was demonstrated that cyclic plasticity persisted in the material near the crack tip. The cyclic plasticity was reduced but not negligible when the crack was closed. The traditional approaches may have overestimated the effect of crack closure in fatigue crack growth predictions.     

Stress analysis of an orthotropic material under diametral compression

The diametral compression test is commonly used to determine the tensile strength of brittle materials. For isotropic materials a simple relation based on specimen geometry and the applied load at failure is used to calculate the tensile strength. Previous to this work the effect of material orthotropy and material orientation on the specimen stress state had not been completely determined. In this study, both isotropic and orthotropic specimens were analyzed using a finite element analysis and experimentally verified by strain gage and photoelastic measurements. Further, this work investigated the effect of the applied load area on the specimen stress state. Results of this work show that there is a significant difference between the theoretical calculations based on the assumption of material isotropy when compared to an orthotropic material. This difference can be as much as 45 percent depending on the degree of orthotropy and the orientation. It was also determined that the applied load area and material orientation significantly influence the specimen stress state. An applied load area of 8 percent of the circumference was found to reduce the stresses in the applied load region.     

A viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature

Viscoplastic crack-tip deformation behaviour in a nickel-based superalloy at elevated temperature has been studied for both stationary and growing cracks in a compact tension (CT) specimen using the finite element method. The material behaviour was described by a unified viscoplastic constitutive model with non-linear kinematic and isotropic hardening rules, and implemented in the finite element software ABAQUS via a user-defined material subroutine (UMAT). Finite element analyses for stationary cracks showed distinctive strain ratchetting behaviour near the crack tip at selected load ratios, leading to progressive accumulation of tensile strain normal to the crack-growth plane. Results also showed that low frequencies and superimposed hold periods at peak loads significantly enhanced strain accumulation at crack tip. Finite element simulation of crack growth was carried out under a constant ΔK-controlled loading condition, again ratchetting was observed ahead of the crack tip, similar to that for stationary cracks.A crack-growth criterion based on strain accumulation is proposed where a crack is assumed to grow when the accumulated strain ahead of the crack tip reaches a critical value over a characteristic distance. The criterion has been utilized in the prediction of crack-growth rates in a CT specimen at selected loading ranges, frequencies and dwell periods, and the predictions were compared with the experimental results.     

Nonequilibrium thermal/mechanical response of 6061 aluminum alloy at elevated temperature

This work is concerned with the thermal/mechanical characterization of the 6061 aluminum alloy stretched uniaxially in an elevated temperature environment. The resulting response is one of nonequilibrium where each local element reacts differently in terms of stress, strain and temperature. That is, the local strain and temperature rate change from one location to another with time. While the initial temperature in both the specimen and its surrounding are kept constant, thermal oscillation occurs when the specimen is strained uniaxially. The temperature in the solid decreases at first below the reference state and then increases. A reversal of heat flow takes place between the specimen and surrounding medium which typifies the nonequilibrium character of thermal/mechanical behavior in uniaxial specimens.Numerical results are obtained for loading rate of 1.27 × 10⁻⁴cm/s with initial equilibrium temperature of 25°, 75°, 125° and 175° C. Determined are the nonequilibrium conditions in the solid and on the surface. This is accomplished by considering a two-phase medium such that the surrounding air or gas can interact with the solid, both thermally and mechanically. The state of affairs at or near the solid/gas interface are transient in character; they cannot be preassigned as boundary conditions. The a priori specification of temperature and/or its gradient on solid cannot be justified as it can seriously affect analytical predictions.     

Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental–Numerical Method

A new experimental technique has been developed to investigate the onset of fracture in metals at low and intermediate stress triaxialities. The gage section of a flat specimen has been designed such that cracks are most likely to initiate within the specimen center, remote from the specimen boundaries. Along with the specimen, a biaxial testing device has been built to apply a well-defined displacement field to the specimen shoulders. The stress state within the specimen is adjusted by changing the biaxial loading angle. Using this new experimental technique, the crack initiation in metals can be studied experimentally for stress triaxialities ranging from 0.0 to 0.6. The stress and strain fields within the specimen gage section are determined from finite element analysis. The reliability of the computational model of the test set-up has been verified by comparing the simulation results with laser speckle-interferometric displacement measurements during testing. Sample experiments have been performed on the Al-7Si-Mg gravity die casting alloy. A three-step hybrid experimental–numerical calibration procedure has been proposed and applied to determine a phenomenological crack formation criterion for the Al-7Si-Mg alloy.

Hybrid stress analysis of perforated composites using strain gages

A strain gage hybrid method is described for determining individual stresses on the boundary and in the neighborhood of cutouts in orthotropic composites. Results agree with independent measurements and finite element analysis. Few measured strain data are needed, and the measured strains originate away from the hole. Ability to determine the stresses on the edge of a cutout from nonboundary measurements recognizes the difficulties in obtaining reliable measurements very near an edge while circumventing the challenge of attempting to bond gages to the transverse curved surface of a small hole or notch. The method also alleviates the problem of not knowing a priori where the most serious stress will occur on the geometric boundary and, hence, where to locate strain gages.     

Analytical and experimental determination of dynamic impact stress intensity factor for 40 Cr steel

A linear elastic three-dimensional finite element analysis is made to analyze the near field stress behavior of an edge cracked rectangular bar simply supported and subjected to central impact at the back side of the crack. The material is made of 40 Cr steel. Determined numerically are the local time histories of the stress wave, displacement near load point, crack tip strain, and dynamic stress intensity factor K_(d)¹. The above quantities were also measured experimentally by performing impact tests; they agreed well with the analytical results and determine the load at fracture initiation and hence the critical dynamic stress intensity factor K_(d)^1c. The interaction effect between the loading bar and specimen appears to be negligible.     

Whole-field strain measurement in a pin-loaded plate by electronic speckle pattern interferometry and the finite element method

The strain field in an epoxy plate loaded in tension through a steel pin is determined using electronic speckle pattern interferometry (ESPI) and the finite element method (FEM). In a dual-beam illumination speckle interferometer, the in-plane component of the displacement at the plate's surface is accurately measured using a four-step phase-shifting algorithm. Digital image processing algorithms have been developed for noise reduction and strain calculation directly in the computer from the phase map with a strain gage length of about 0.4 mm. A whole-field strain map is obtained, as well as distributions of strain concentration factor, in critical regions near the hole of the plate. FEM is used to perform a nonlinear contact analysis accounting for friction effects at the pin/hole interface. The agreement between experimental results and numerical predictions is good. In terms of speed, accuracy and ease of use, dual-beam ESPI appears to be a superior method of whole-field strain analysis.     

Compliance rate change of tapered double cantilever beam specimen with hybrid interface bonds

This paper presents a combined numerical and experimental study of compliance rate change of Tapered Double Cantilever Beam (TDCB) specimens for Mode-I fracture of hybrid interface bonds. The easily machinable TDCB specimen, which is designed to achieve a constant rate of compliance change with respect to crack length, is developed for Mode-I fracture tests of hybrid material bonded interfaces, such as wood bonded to fiber-reinforced plastic (FRP) composite. The linearity of compliance crack-length relationship of the specimen is verified by both Rayleigh–Ritz method and finite element analysis. An experimental compliance calibration program for specimens with wood–wood and FRP–FRP bonded interfaces is carried out, and a constant rate change of compliance with respect to crack length is obtained for a specific range of crack length. Fracture tests are further performed using TDCB specimens for wood–wood and wood–FRP bonded interfaces to determine the critical loads for crack initiation and crack arrest, and using the constant compliance rate change of the specimens determined by experiment or analysis, the respective critical strain energy release rates, or fracture energies, are obtained. This study indicates that the constant compliance rate change obtained from experiment or finite element analysis for linear-slope TDCB specimens can be used with confidence for fracture studies of hybrid material interface bonds.     

Fracture prediction in stretch forming using finite element simulation combined with ductile fracture criterion

Summary  A criterion for ductile fracture is introduced in the finite element simulation of sheet metal forming. From the calculated histories of stress and strain in each element, the fracture initiation site and the critical stroke are predicted by means of the ductile fracture criterion. The calculations are carried out for axisymmetric stretch forming of various aluminium alloy sheets and their laminates clad by mild steel sheets. The predictions so obtained are compared with experimental observations. The results show that the combination of the finite element simulation and the ductile fracture criterion enables the prediction of forming limit in a wide range of sheet metals. Accepted for publication 11 August 1996     

Mechanical Characterization of Biological Membranes with Moiré Techniques and Multi-Point Simulated Annealing

This paper describes an hybrid procedure for mechanical characterization of biological membranes. The in-plane displacement field of a glutaraldehyde treated bovine pericardium patch obtained with an equi-biaxial tension test is measured with intrinsic moiré and then compared with finite element predictions. Preliminary analysis of moiré patterns observed in the experiments justifies the assumption of the constitutive model based on transversely isotropic hyperelasticity. In order to determine the 16 hyperelastic constants included in the constitutive model and the fiber orientation, the difference Ω between displacement values measured with moiré and their counterpart determined numerically is minimized by means of multi-level and multi-point simulated annealing. Results clearly demonstrate the efficiency of the identification procedure presented in this research: in fact, residual difference between experimental data and numerical values of in-plane displacements is less than 2%. In order to validate the entire identification process, another experimental test is conducted by inflating the same specimen. Out-of-plane displacements, now measured with projection moiré, are compared with predictions of a new finite element model reproducing the experimental test. The 16 hyper-elastic constants previously determined are given in input to the inflation test FE model. Remarkably, experimental and numerical results are again in excellent agreement: maximum percent error on w-displacement is less than 3%.     

Boundary Effects in the Eigenstrain Method

We present a comprehensive study of the effects of internal boundaries on the accuracy of residual stress values obtained from the eigenstrain method. In the experimental part of this effort, a composite specimen, consisting of an aluminum cylinder sandwiched between steel cylinders of the same diameter, was uniformly heated under axial displacement constraint. During the experiment, the sample temperature and the reaction stresses in the load frame in response to changes in sample temperature were monitored. In addition, the local (elastic) lattice strain distribution within the specimen was measured using neutron diffraction. The eigenstrain method, utilizing finite element modeling, was then used to predict the stress field existing within the sample in response to the constraint imposed by the load frame against axial thermal expansion. Our comparison of the computed and measured stress distributions showed that, while the eigenstrain method predicted acceptable stress values away from the cylinder interfaces, its predictions did not match experimentally measured values near them. These observations indicate that the eigenstrain method is not valid for sample geometries with this type of internal boundaries.     

Measurement of Torsionally Induced Shear Stresses in Shrink-Fit Assemblies

Shear stresses along the shaft/hub interface in shrink-fit components, generated by torsional loads, can drive premature failure through fretting mechanisms. It is difficult to numerically predict these shear stresses, and the associated circumferential slip along the shaft/hub interface, due to uncertainties in frictional behaviour and the presence of steep stress gradients which can cause meshing problems. This paper attempts to provide validation of a numerical modelling methodology, based on finite element analysis, so the procedure may be used with confidence in fitness-for-purpose cases. Very few experimental techniques offer the potential to make measurements of stress and residual stress interior to metallic components. Even fewer techniques provide the possibility of measuring shear stresses. This paper reports the results of neutron diffraction measurements of shear stress and residual shear stress in a bespoke test specimen containing a shrink-fit. One set of measurements was made with a torsional load ‘locked-in’. A second set of measurements was made to determine the residual shear stress when the torsional load had been applied and removed. Overall, measurement results were consistent with numerical models, but the necessity for a small test specimen to allow penetration of the neutron beam to the measurement locations meant the magnitude of shear stresses was at the limits of what could be measured experimentally.     

Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens

Nonlinear dynamic finite element analysis (FEA) is conducted to simulate the fracture of unnotched Charpy specimens of steel under pendulum impact loading by a dedicated, oversized and nonstandard Bulk Fracture Charpy Machine (BFCM). The impact energy needed to fracture an unnotched Charpy specimen in a BFCM test can be two orders of magnitude higher than the typical impact energy of a Charpy V-notch specimen. To predict material failure, a phenomenological, stress triaxiality dependent fracture initiation criterion and a fracture evolution law in the form of strain softening are incorporated in the constitutive relations. The BFCM impact energy results obtained from the FEA simulations compare favorably with the corresponding experimental data. In particular, the FEA predicts accurately the correlations of the BFCM impact energy with such factors as specimen geometry, impactor tup width and material type. The analyses show that a specimen’s progressive deterioration through the thickness dimension displays a range of shear to ductile fracture modes, demonstrating the necessity of applying a stress state dependent fracture initiation criterion. Modeling the strain softening behavior helps to capture the residual load carrying capability of a ductile metal or alloy beyond the onset of damage. The total impact energy can be significantly under predicted if a softening branch is not included in the stress-strain curve. This research supports a study of the puncture failure of railroad tank cars under dynamic impact loading. Applications of the presented fracture model in failure analyses of other structures are further discussed.