Residual Stress Gradient Research Articles

Crack arrest in thin metallic film stacks due to material- and residual stress inhomogeneities

Miniaturized materials, in general, exhibit higher strength compared to their bulk counterparts. As a consequence, their resistance to fracture is often compromised. However, the effect of material inhomogeneities can be used to significantly improve the fracture toughness of thin film components. In this work, the material inhomogeneity effect on the crack driving force, caused by material property and residual stress variations in thin tungsten and copper stacks, is numerically investigated. To this purpose, a finite element analysis is performed using the concept of configurational forces. In this way, we are able to distinguish between the various inhomogeneity effects and draw conclusions about the effective crack driving force. It is demonstrated that the material inhomogeneity effect is not solely determined by the material property variations at the interfaces, since an important contribution emerges due to a smooth residual stress gradient within the layers. The possibility to separate the different effects represents an opportunity for cost efficient design of future reliable thin film microelectronic components.

Preventing delayed cracks in SUS304 deep drawn cups using extreme blank holding forces aided by nanolubrication

Disappearance and reappearance of delayed cracks were observed in deep drawing process of SUS304 cylindrical cups under elevated blank holding forces (BHF) of 8~32 kN with nanolubricants containing 1~3 wt% SiO2 concentrations at limiting draw ratio. The widest crack-free BHF range determined experimentally, i.e., 29~31 kN was for 2 wt% SiO2. Delayed cracks were observed below and beyond this BHF range. The frictional force at the flange surfaces slightly increased when entering the crack-free BHF range, as evidenced by the rebound in sidewall thickness, relative intensity of α′-martensite, elongated height, and drawing force beyond 28 kN. The coefficients of friction for each BHF were obtained with finite element simulations. Since residual stresses developed along the outer surface of the cup due to the unbending of the material when the material left the draw die profile, the slight increase in frictional force in the radial direction along the flange surfaces reduced the circumferential tensile residual stress of the cup, particularly at 80% cup height. The elimination of delayed cracks was attributed to the lower tensile residual stress gradient, i.e., lower and higher tensile residual stresses at 80% and 100% cup heights, respectively. However, the excessive increase at 100% cup height was a result of the increase in longitudinal compressive stress at BHF beyond 31 kN due to the stress equilibrium, leading to the reappearance of cracks. The minimum BHF required to eliminate cracks changed minimally with increasing SiO2 concentration.

The influence of node coupling on welding deformation and residual stress of T-joint welding root

High accuracy and high efficiency is the key to the application of structural welding simulation. To explore the influence of welding root node coupling on the precision of finite element establishing model, the finite element model of T-joint with coupling and uncoupling of nodes in welding root is established. The welding deformation and residual stress distribution of T joint are obtained, and the test results are verified. The results show that, from the trend, the welding deformation and residual stress results are all consistent with the distribution trend of measured results, which proves the correctness and validity of the finite element model. The maximum error of the node uncoupling calculation results and the experimental results is 5.4%, and the maximum error of the node coupling calculation results is 12.2%. The results of the welding root node uncoupling are more close to the actual measurement results. At the same time, the residual stress gradient near the weld seam and heat affected zone changes greatly, and the coupling of the welding root nodes has little influence on the residual stress distribution, and there are three wave peaks. The two treatments have the same trend of stress distribution curve, and the peak value is similar. The peak value of residual stress of node coupling is 303.9MPa, and the peak value of residual stress of node uncoupling is 304.5MPa. The error between welding root node uncoupling and the test result is 4.9%, and the error of node coupling is 7.7%. Therefore, it is suggested that the welding root of T-joint should be node coupling. The research results have important guiding significance for improving the prediction accuracy of welding simulation.

Residual stress gradient and relaxation upon fatigue deformation of diamond-like carbon coated aluminum alloy in air and methanol environments

Amorphous diamond-like carbon coating (DLC) of 2 μm in thickness was deposited over the aluminum alloy substrate using magnetron sputtering deposition technique. In order to understand the efficacy of coating deposition, coated specimens were subjected to rotating bending fatigue in air and methanol environments respectively. Raman spectroscopy was used in conjunction with grazing incidence X-diffraction technique to obtain depth-resolved residual stress gradients of coated-aluminum substrate. The residual stress generated due to coating deposition was calculated using Raman spectroscopy and it was −1.13 ± 0.16 GPa (compressive in nature). Furthermore, Raman spectroscopy was utilized for the quantification of stress relaxation upon fatigue loading in air and methanol environments. It was observed that the irrespective of the testing environment, good correlation exists between the stress relaxation magnitude and number of cycles endured before failure.

Finite Element Analysis Simulation of the Effect of Induction Hardening on Rolling Contact Fatigue

The objective of this research is to conduct a finite element analysis to better understand the effects of induction hardening on rolling contact fatigue (RCF). The finite element analysis was developed in three-dimensional to estimate the maximal loading and the positions of the crack nucleation sites in the case of cylinder contact rolling. Rolling contact with or without surface compressive residual stress (RS) were studied and compared. The RS profile was chosen to simulate the effects of an induction hardening treatment on a 48 HRC tempered AISI4340 steel component. As this hardening process not only generates a RS gradient in the treated component but also a hardness gradient (called over-tempered region), both types of gradients were introduced in the present model. RSs in compression were generated in the hard case (about 60 HRC); tension values were introduced in the over-tempered region, where hardness as low as 38 HRC were set. In order to estimate the maximal allowable loadings in the rotating cylinders to target a life of 106 cycles, a multiaxial Dang Van criterion and a shear stress fatigue limit were used in the positive and negative hydrostatic conditions, respectively. With the proposed approach, the induction hardened component was found to have a maximal allowable loading significantly higher than that obtained with a nontreated one, and it was observed that the residual tensile stress peak found in the over-tempered region could become a limiting factor for fatigue rolling contact life.

Biaxial fatigue property enhancement of gradient ultra-fine-grained Zircaloy-4 prepared by surface mechanical rolling treatment

Surface mechanical rolling treatment (SMRT) was applied to modify the microstructure and biaxial fatigue properties of Zircaloy-4 tubes. Gradient ultra-fine microstructural layers of ~ 500 μm in-depth from the outside surface were fabricated on rods. Residual compressive stresses with gradient distribution were simultaneously produced. Biaxial tension–torsion fatigue test was conducted to assess the effect of modified microstructures and residual stress on the fatigue lifetime and deformed substructure of Zircaloy-4. The results show that the SMRT Zircaloy-4 alloy possesses more than double biaxial fatigue lifetime than that of the as-received Zircaloy-4 without SMRT at a tension–torsion stress ratio of 1.0. Microstructural examination reveals that the SMRT Zircaloy-4 alloy shows sequential deformation characteristics at different layers across the tubular wall during biaxial fatigue. The fatigued dislocation configuration changes from dislocation cells within the depth of 200 μm, to bent lamellar structures at the depth of ~ 300 μm, and embryonic dislocation cells at the depth of ~ 500 μm. The enhancement of biaxial fatigue life in the SMRT Zircaloy-4 can be attributed to the combined effects of the gradient ultra-fine structure and the gradient residual compressive stress in the vicinity of surface suppress the fatigue crack initiation and propagation.

Evaluation of Rolling Contact Fatigue of a Carburized Wind Turbine Gear Considering the Residual Stress and Hardness Gradient

Carburized gears are applied extensively in large-scale heavy duty machines such as wind turbines. The carburizing and quenching processes not only introduce variations of hardness from the case to the core but also generate a residual stress distribution, both of which affect the rolling contact fatigue (RCF) during repeated gear meshing. The influence of residual stress distribution on the RCF risk of a carburized wind turbine gear is investigated in the present work. The concept of RCF failure risk is defined by combining the local material strength and the multi-axial stress condition resulting from the contact. The Dang Van multi-axial fatigue criterion is applied. The applied stress field is calculated through an elastic-plastic contact finite element model. Residual stress distribution and the hardness profile are measured and compared with existed empirical formula. Based upon the Pavlina–Tyne relationship between the hardness and the yield strength, the gradient of the local material strength is considered in the calculation of the RCF failure risk. Effects of the initial residual stress peak value and its corresponding depth position are studied. Numerical results reveal that compressive residual stress (CRS) is beneficial to RCF fatigue life while tensile residual stress (TRS) increases the RCF failure risk. Under heavy load conditions where plasticity occurs, the accumulation of the plastic strain within the substrate is significantly affected by the initial residual stress distribution.

A multireflection and multiwavelength residual stress determination method using energy dispersive diffraction

The main focus of the presented work was the investigation of structure and residual stress gradients in the near-surface region of materials studied by X-ray diffraction. The multireflection method was used to measure depth-dependent stress variation in near-surface layers of a Ti sample (grade 2) subjected to different mechanical treatments. First, the multireflection grazing incidence diffraction method was applied on a classical diffractometer with Cu Kα radiation. The applicability of the method was then extended by using a white synchrotron beam during an energy dispersive (ED) diffraction experiment. An advantage of this method was the possibility of using not only more than one reflection but also different wavelengths of radiation. This approach was successfully applied to analysis of data obtained in the ED experiment. There was good agreement between the measurements performed using synchrotron radiation and those with Cu Kα radiation on the classical diffractometer. A great advantage of high-energy synchrotron radiation was the possibility to measure stresses as well as the a0 parameter and c0/a0 ratio for much larger depths in comparison with laboratory X-rays.

Control of the residual stress gradients in copper films by inert ion implantation

In this work, we studied the effect of inert ion implantation using helium and xenon ions on residual stress gradients in copper films. A copper microcantilever beam array was fabricated on a (1 0 0) silicon wafer by conventional bulk micromachining. The as-fabricated copper microcantilevers showed upward bending deformation as a result of positive residual stress gradient in films. Helium and xenon ions were implanted at various doses and energies into microcantilevers before releasing them from substrates. The magnitudes and signs of residual stress gradients were effectively controlled by both helium and xenon ion implantation and depended on implantation energy and ionic dosages. The mechanism of residual stress control appeared to involve counterbalancing residual stress gradients with compressive residual stresses induced by volume expansions of implanted regions and the direct effect of surface modification by ion bombardment.

Plastic strain recovery in nanocrystalline copper thin films

Plastic strain recovery is a distinctive behavior of nanocrystalline thin film metals whereby plastic strain induced via application of an external load is gradually recovered over a time period of hours to days after load removal. Previous studies to model plastic strain recovery assumed that grain boundary sliding or grain boundary diffusion with heterogeneous diffusivity was the dominant deformation mechanism. In this study we propose that grain boundary diffusion in the presence of nanoscopic voids can lead to plastic strain recover without having to assume a sliding or heterogeneous diffusivity on grain boundaries. To model the system numerically in the context of the finite element method, we include a diffusion zone (DZ) and a cohesive zone (CS) on the grain boundaries and also include the possibility of plastic deformation in the surrounding grains. Our results suggest that diffusion leads to a mass flux toward the “void tips” (i.e. intersections of the voids and grain boundaries) as the external load is applied. Upon removal of the load, the additional material that accumulated near the void tips introduces a compressive residual normal stress on the grain boundary. The gradient of grain boundary residual stress leads to diffusion flux away from the void tip along the grain boundary in addition to diffusion flux to the void surface from the grain boundary. This redistribution of mass leads to a reduction in specimen length that is interpreted in terms of plastic strain recovery. With time the diffusion flux reduces the grain boundary stress gradient to the point where further grain boundary diffusion flux becomes negligible, after which diffusion flux occurs predominantly from the grain boundary at the void tip to the void surface. Since only one mass flux route remains active, the predicted plastic strain recovery rate is smaller. These simulation results are consistent with our experimental results that indicate plastic strain recovery exhibits two characteristic rates: a “fast” strain rate of about [10−7]s−1 followed by transition to a “slow” strain rate of about [10−9]s−1.

On the Simulation Scalability of Predicting Residual Stress and Distortion in Selective Laser Melting

Rapid heating and cooling thermal cycle of metals in selective laser melting (SLM) generates high tensile residual stress which leads to part distortion. However, how to fast and accurately predict residual stress and the resulted part distortion remains a critical issue. It is not practical to simulate every single laser scan to build up a functional part due to the exceedingly high computational cost. Therefore, scaling up the material deposition rate via increasing heat source dimension and layer thickness would dramatically reduce the computational cost. In this study, a multiscale scalable modeling approach has been developed to enable fast prediction of part distortion and residual stress. Case studies on residual stress and distortion of the L-shaped bar and the bridge structure were presented via the deposition scalability and validation with the experimental data. High residual stress gradient in the building direction was found from high tensile on the surface to high compressive in the core. The part distortion can be predicted with reasonable accuracy when the block thickness is scaled up by 50 times the layer thickness from 30 μm to 1500 μm. The influence of laser scanning strategy on residual stress distribution and distortion magnitude of the bridges has shown that orthogonal scanning pattern between two neighboring block layers is beneficial for reducing part distortion.

Investigation of the Effect of Residual Stress Gradient on the Wear Behavior of PVD Thin Films

The control of residual stresses has been seldom investigated in multilayer coatings dedicated to improvement of wear behavior. Here, we report the preparation and characterization of superposed structures composed of Cr, CrN and CrAlN layers. Nano-multilayers CrN/CrAlN and Cr/CrN/CrAlN were deposited by Physical Vapor Deposition (PVD) onto Si (100) and AISI4140 steel substrates. The Cr, CrN and CrAlN monolayers were developed with an innovative approach in PVD coatings technologies corresponding to deposition with different residual stresses levels. Composition and wear tracks morphologies of the coatings were characterized by scanning electron microscopy, high-resolution transmission electron microscopy, atomic force microscopy, x-ray photoelectron spectroscopy, energy-dispersive x-ray spectroscopy, x-ray diffraction and 3D-surface analyzer. The mechanical properties (hardness, residual stresses and wear) were investigated by nanoindentation, interferometry and micro-tribometry (fretting-wear tests). Observations suggest that multilayer coatings are composed mostly of nanocrystalline. The residual stresses level in the films has practically affected all the physicochemical and mechanical properties as well as the wear behavior. Consequently, it is demonstrated that the coating containing moderate stresses has a better wear behavior compared to the coating developed with higher residual stresses. The friction contact between coated samples and alumina balls shows also a large variety of wear mechanisms. In particular, the abrasive wear of the coatings was a combination of plastic deformation, fine microcracking and microspallation. The application of these multilayers will be wood machining of green wood.

Residual Stress in Metal Additive Manufacturing

Additive manufacturing (AM) has been widely used to fabricate functional metal parts in automobile, aerospace, energy, and medical device industries due to its flexible process capacity including complex geometry, functional graded materials, and free usage of tool. For the two major categories of metal additive manufacturing processes include powder bed fusion (PBF) and directed energy deposition (DED), parts are fabricated through melting of feed stock materials in the form of either powders or wires directly from a CAD model. The unique thermal cycle of metal additive manufacturing is characterized by: (1) rapid heating rate due to high energy intensity with steep temperature gradients; (2) rapid solidification with high cooling rates due to the small volume of melt pool; and (3) melt-back involving simultaneous melting of the top powder layer and re-melting of underlying previously solidified layers. Residual stress caused by the unique thermal cycle in AM is the critical issue for the fabricated metal parts since the steep residual stress gradients generate part distortion which dramatically deteriorate functionality of the end-use parts. This paper comprehensively assessed the current research status on residual stress sources, characteristics, and mitigation. First, the relationship between residual stress and microstructure is highlighted in AM metal parts. Then, the measurement methods and characteristics of residual stress in both as-build metal parts and post-processed ones were summarized. Third, residual stress mitigation and control methods including in-situ and post-process control methods were thoroughly discussed. Furthermore, future work directions are provided in this work.

A scalable predictive model and validation for residual stress and distortion in selective laser melting

The unique thermal cycle of rapid melting, solidification, and melt-back in selective laser melting (SLM) induces steep residual stress gradients which lead to part distortion. However, it is extremely difficult to predict residual stress in SLM due to complex multi-physics phenomena and scale-up of millions of laser scans. This paper has developed a geometry scalable predictive model across microscale laser scan, mesoscale layer hatch, and macroscale part build-up to fast predict residual stress in different scanning strategies. The predictions were validated using the L-shaped bar and bridge structures. The geometry scalability law provides an effective tool for optimizing part designs.

Residual stress induced convex bending in laser peen formed aluminum alloy

Laser peen forming is a purely mechanical forming method developed to accurately bend, shape, precision align, or repair components using nanosecond-pulsed laser induced shock waves. This paper aims to clarify the residual stress induced bending process in laser peen formed aluminum alloy plates. Finite element simulations were performed to investigate the bending angle and residual stress redistribution before and after bending. A reasonable agreement between simulation and experiment results was achieved. The results showed that larger bending angle was obtained by increasing the number of laser impacts and laser peened area. Besides, the bending angle in 3 mm plates was larger than that in 2 mm plates under the same processing condition. The laser peening induced bending angle is controlled by a residual stress gradient in the thickness direction.

30 nm X-ray focusing correlates oscillatory stress, texture and structural defect gradients across multilayered TiN-SiOx thin film

Resolving depth gradients of microstructure and residual stresses within individual sublayers of multilayered thin films and understanding their origin as well as their influence on functional properties are challenging tasks. In this work, a newly developed synchrotron focusing setup based on Multilayer Laue Lenses, providing an X-ray beam diameter of ∼30 nm, is used to characterize the cross-sectional properties of a 2.9 μm thick sculptured multilayered TiN-SiOx film, which consists of twelve ∼230 nm thick nano-crystalline TiN sublayers of zigzag columnar grain morphology separated by eleven amorphous SiOx sublayers, both prepared by oblique magnetron sputtering on a Si(100) substrate. The X-ray nano-diffraction analysis of the TiN sublayers reveals (i) an oscillatory variation of compressive residual stresses across the film ranging between −1.8 and −0.25 GPa, (ii) the presence of <100> fiber textures with three different fiber axis orientations, which abruptly change between the individual sublayers, and (iii) gradually decreasing densities of structural defects within every TiN sublayer, exhibiting a sawtooth-like depth-profile across the film. The near-substrate TiN sublayer shows the highest compressive stress reaching ∼ −1.8 GPa, a unique texture and the largest density of defects among all sublayers, which indicates diverse nucleation mechanisms of TiN on the native Si oxide and on the SiOx sublayers. The results demonstrate that the average stress state and the microstructure within the individual TiN sublayers can be influenced effectively by the applied deposition conditions, although self-organization processes during the sublayers' evolution give rise to the occurrence of qualitatively similar gradual trends, which differ in intensity and which were characterized also by complementary laboratory X-ray diffraction, as well as scanning and transmission electron microscopies. Finally, the presented results document that the novel X-ray nano-probe approach allows for the characterization of nano-scale gradients within individual microstructural features of polycrystalline thin films and pioneers the way for knowledge-based synthesis of thin films with predefined cross-sectional microstructure and property gradients.

Gradient residual strain and stress distributions in a high pressure torsion deformed iron disk revealed by high energy X-ray diffraction

High energy X-ray diffraction is used to investigate for the first time the distribution of residual X-ray elastic stresses inside a high pressure torsion (HPT) deformed iron disk with a diameter and thickness of ~30 and ~8mm, respectively. In the experiment, a dedicated conical slit system restricts the diffraction gauge volume in three dimensions to ~0.45mm3, which is then used to scan the bulk sample cross-section in a non-invasive manner. Pronounced residuals stress gradients with maximal tensile stresses of ~200MPa are observed along radial and tangential directions and are correlated to the deformation gradient arising from HPT.

Residual stress gradient of Cr and CrN thin films

In this work Cr, CrN thin films were grown by the Magnetron Sputtering technique on monocrystalline silicon (400) substrates. Also, a (Cr/CrN)2 multilayer film was grown in order to compare the values of stress between multilayer and single layers. The total thickness of all films was approximately equal to 1 μm. Structural characterization and residual stress measurements were performed by the grazing X-ray diffraction method and the data were collected at LNLS - Brazilian Synchrotron Light Laboratory. Different angles of incidence were selected in order to obtain values of residual stress at different penetration depths. A linear model of residual stress as a function of the depth profile from experimental data was obtained by using the Laplace transform. Results indicate smaller tensile residual stress at surface and higher stresses at film/substrate interface for the Cr monolayer and for the CrN phase in the (Cr/CrN)2 multilayer. On the contrary, the CrN film presented higher tensile stresses at surface.

Resolving alternating stress gradients and dislocation densities across AlxGa1-xN multilayer structures on Si(111)

Gradients of residual stresses and crystal qualities across a 2 μm thick AlN/Al0.32Ga0.68N/GaN/Al0.17Ga0.83N multilayer stack deposited on Si (111) were evaluated by combining the following techniques: High-resolution X-ray diffraction (XRD), scanning transmission electron microscopy (STEM), high resolution transmission electron microscopy, and ion beam layer removal method (ILR) with 100 nm depth resolution. ILR reveals the alternating stress profiles, which are related to sublayer dislocation-density gradients. The laboratory XRD confirms the derived mean stress values, the presence of stress gradients within the sublayers, and decreasing average sublayer threading dislocation-densities across the heterostructure. Additionally, the decreasing dislocation-densities within the individual sublayers are visualized by STEM. The documented stepwise improved crystal quality enables the formation of a highly tensile stressed 20 nm thick Al0.17Ga0.83N top barrier layer, resulting in a pseudomorphic GaN/Al0.17Ga0.83N interface.

Residual stress analysis of energy-dispersive diffraction data using a two-detector setup: Part II — Experimental implementation

Based on the theoretical concept of a two-detector setup for the energy-dispersive diffraction method (Apel et al., 2017), the experimental implementation of the proposed measurement concepts is demonstrated. The measurement configurations as well as the formalism for data evaluation introduced in the first part of this series are applied to the analysis of in- and out-of-plane near surface residual stress gradients in mechanically surface treated steel. Diffraction experiments carried out with the Bremsstrahlung of a conventional X-ray tube are shown to yield results with a quality comparable to measurements conducted at a synchrotron beamline. Furthermore, it is demonstrated that the simultaneous measurement of the positive and the negative ψ-branch can partly compensate for the much higher counting times due to the lower photon flux of the X-ray tube. The results are compared and assessed with those obtained by means of synchrotron radiation (beamline EDDI@BESSY II) and the layer removal method (LRM).