Thermally-induced Residual Stresses Research Articles

Hyperelastic constitutive relations for soft elastomers with thermally-induced residual stress

Residual stress widely exists in soft materials. Besides growth, inhomogeneous thermal expansion is also a primary cause of residual stress. However, establishing a proper hyperelastic constitutive relation is a great challenge since the existing theories cannot capture the change of underlying mechanical responses triggered by temperature variations. In this paper, a general hyperelastic constitutive relation for soft elastomers with thermally-induced residual stress is developed. We first reveal the initial temperature dependence of conventional thermoelastic models. This property attributes the alteration of the underlying thermoelastic response to free thermal expansions. Then, a compatibility-broken curvature compensation (CBCC) framework is established based on finite thermoelasticity. It generates a free thermal expansion to eliminate the Riemannian curvatures of the virtual stress-free configuration derived from the isothermal stress release. Such a mechanism indicates the non-local effect of the residual stress, which fundamentally modifies the traditional view that invariant formulations cover all the possible functional dependence of residual stress. Also, the obtained governing equations are similar to Einstein field equations of the general theory of relativity. This similarity may deeply imply a standard mechanism concerning the curvature compensation leading to residual stress genesis. We finally conduct comparative analyses of the spherically symmetric and axisymmetric problems between the current constitutive relation and the existing models. The influences of adopting distinct residual stresses, the performance of the non-local effect, and the availability of the new constitutive relation are investigated in detail. This framework can shed some light on the constitutive modeling of soft materials.

Measurement and simulation of thermal-induced residual stresses within friction stir lapped Al/steel plate

Welding residual stress and distortion usually affect the assembly accuracy, product performance, and service life, with no exception for the Al/steel hybrid structure. The lapped joint of 5052 Al alloy and DP590 steel was made by friction stir welding (FSW) at various rotation speeds. A subsequentially coupled computational modeling approach based on the in-house software JWRIAN combining an efficient hybrid solution method was developed to predict the temperature field, the residual stress distribution and the warpage deformation. Based on the simulation, a higher welding temperature with subsequently a higher average cooling rate was created at a high rotation velocity, leading to the area extension of the longitudinal tensile stress and transverse compressive stress near the weld zone. The thermal expansion coefficient mismatch leads to the mirroring distribution of the near interfacial residual stress on both sides, particularly for transverse residual stress. With the increasing rotation speed, the longitudinal residual stress on the steel side near the interface was changed from compressive to the tensile state. The maximum warpage deformation in the Al plate border became larger at a higher rotation speed. The surface residual stress was measured by X-ray diffusion method and the internal residual stress was reconstructed by the contour method with the aid of elastic FE analysis. The comparisons of temperature history, residual stress and deformation indicated satisfactory agreements between simulation and experiment ones.

Simultaneous optimisation of support structure regions and part topology for additive manufacturing

Support structures are required to enable the build of additively manufactured parts. The supports reinforce overhanging regions on the part and/or counteract the thermally-induced residual stresses generated during printing. However, the optimal design of the part for its intended use case is decoupled from the design of the support structures in a conventional design for additive manufacturing (DfAM) workflow. In this work, a novel methodology is presented that simultaneously optimises the part topology and its support structure regions. A two-model topology optimisation approach is considered. One model describes the combined part and support structure regions subject to a pseudo-gravity load and a second model describes the part subject to its intended application load cases. A novel load-aligned trunk and branch support structure is generated from the topology optimisation results. Generating the fine support features in a post-processing step avoids the computational expense of topology optimising the intricate supports directly. Thermo-mechanical simulations of a selective laser melting process confirms that this new approach to optimising support structures can reduce manufacturing process-induced deformation when benchmarked against a conventional DfAM workflow.

Design optimization of thermally conductive support structure for laser powder-bed fusion process with part-scale thermal history

Although there has been a substantial volume of research for mitigating the thermally-induced residual stress with the heat accumulation in powder bed fusion (PBF) process, it has been challenging to quantify, access, and optimize the heat dissipation at part-scale. Furthermore, a practical method of designing three-dimensional support with a reasonable index for evaluating inhomogeneous cooling is also of high importance for facilitating the process. In this study, an optimization methodology for designing a thermally conductive lattice support structure is proposed considering the layerwise heating and cooling in the PBF process. A part-scale numerical model with homogenized properties of lattice material is constructed using the temperature-thread multiscale modeling approach to simulate the transient temperature field in PBF process. The transient analysis model is then integrated into the lattice structure topology optimization (LSTO) with the equivalent static loads method (ESLM) based sensitivity analysis to derive the optimal density profile of the support. In particular, a novel concept of the normalized liquid lifetime contour is proposed to analyze the inhomogeneous cooling in PBF process at part-scale. The normalized liquid lifetime is also utilized to build an effective part-scale thermal load to significantly reduce the overall computational cost for the optimization process. The proposed framework is also validated through thermo-mechanical process analysis and experiment for a benchmark case of manufacturing a twin cantilever beam.

Thermal-induced Residual Stresses and Distortions in Friction Stir Welds - A Literature Review

Friction Stir Welding (FSW) is a solid-state welding technique that uses the heat generated from friction to assemble a wide variety of materials. Irrespective of having a lower heat input as compared to conventional welding techniques, friction stir welds are still prone to significant thermal-induced stresses and distortions owing to the uneven heating and cooling cycles that a weld goes through. Surprisingly, not several reviews have addressed both the residual stresses and distortions of friction stir welds despite their crucial impact on the weld performance. Therefore, the current paper reviews their development, their correlation with process parameters, and ways to reduce them. Moreover, it explains the current status of process modeling and research gaps in the area of interest.

Bending strength of ceramic compounds bonded with silicate-based glass solder

AbstractIn the field of dental technology, the length of ceramic pontics is limited to avoid mechanical failure. To reduce thermal-induced residual stress within the ceramic, using smaller subcomponents and subsequent bonding with silicate-based glass solder may be a favorable approach. Thus, the bending strength of zirconia compounds bonded with different silicate-based glass solders was investigated. For this purpose, rectangular specimens made of zirconia were bonded by glass solder. Parameters such as the scarf angle (45° and 90°), two different glass solders, as well as the soldering process (pressure and surface treatment) were varied. All specimens were subjected to quasi-static four-point bending tests according to DIN EN ISO 843-1. Additionally, the quality of the glass solder connection was evaluated usingμCT and fractography. In the present study, zirconia compounds were sucessful bonded of zirconia compounds using silicate-based glass solder was. No significant differences in terms of bending strength were observed with respect to the different bonding parameters analyzed. The highest bending strength of 130.6 ± 50.5 MPa was achieved with a 90° scarf angle combined with ethanol treatment of the specimens before soldering and an additional application of a pressure of 2 bars in a dental pressure pot before subsequent soldering. Nevertheless, the bending strengths were highly decreased when compared to monolithic zirconia specimens (993.4 ± 125.5 MPa).

Microstructure, Residual Stresses, and Strain-Rate-Dependent Deformation and Fracture Behavior of AISI 304L Joints Brazed with NiCrSiB Filler Metals

The knowledge of alloy–process–structure–property relationships is of particular interest for several safety-critical brazed components and requires a detailed characterization. Thus, three different nickel-based brazing filler metals were produced with varying chromium and molybdenum content and were used to braze butt joints of the austenitic stainless steel AISI 304L under vacuum. Two holding times were used to evaluate diffusion-related differences, resulting in six specimen variations. Significant microstructural changes due to the formation and location of borides and silicides were demonstrated. Using X-ray diffraction, alloy-dependent residual stress gradients from the brazing seam to the base material were determined and the thermal-induced residual stresses were shown through simulations. For mechanical characterization, impact tests were carried out to determine the impact toughness, as well as tensile tests at low and high strain rates to evaluate the strain-rate-dependent tensile strength of the brazed joints. Further thermal, electrical, and magnetic measurements enabled an understanding of the deformation mechanisms. The negative influence of brittle phases in the seam center could be quantified and showed the most significant effects under impact loading. Fractographic investigations subsequently enabled an enhanced understanding of the fracture mechanisms.

Multi-material additive manufacturing of functionally graded carbide ceramics via active, in-line mixing

Advanced ceramics are required in many applications including armor, engine components, and wear parts for abrasive, corrosive, and high temperature environments. Heterogeneous structuring in these materials has the potential to unlock extrinsic mechanisms that improve damage tolerance, of vital importance for structural functionality. However, traditional ceramic powder processing and forming techniques limit the design space to simple geometries with chemically homogenous microstructures. Thus, additive manufacturing by direct ink writing (DIW) was applied to fabricate multi-phase carbide specimens with tailored composition and mesostructure. A custom DIW system was developed to allow simultaneous extrusion and mixing of multiple inks, comprised of ceramic particulate suspensions, through a single nozzle. Boron carbide (B4C) and silicon carbide (SiC) were chosen for this study due to their excellent mechanical properties. Aqueous B4C and SiC inks were loaded to 47.5 vol% ceramic content and showed yield-pseudoplastic behavior. The carbide inks were characterized and modified to exhibit similar rheological behavior (yield stress and viscosity), and were used to produce B4C–SiC parts with either discrete or continuous composition variation. Specimens were hot pressed at 35 MPa and 1950 °C, yielding near full density with hardness (Knoop) values of 20–23 GPa. Tailored heterogeneity, achieved via active in-line mixing, is revealed through microstructural characterization. Cracking observed in the specimen with discretely varied composition is the result of thermally-induced residual stress, and is elucidated through analytical calculations.

High-temperature Mechanical Properties and Their Influence Mechanisms of ZrC-Modified C-SiC Ceramic Matrix Composites up to 1600 °C.

In order to understand the influence of the mechanisms of ZrC nanoparticles on the high-temperature mechanical properties of C-SiC ceramic matrix composites, the mechanical properties were measured from room temperature (RT) to 1600 °C under vacuum. The microstructures features were characterized by scanning electron microscopy. In comparison with the composites without ZrC nanoparticles, the ZrC-modified composite presented better mechanical properties at all temperatures, indicating that the mechanical properties could be improved by the ZrC nanoparticles. The ZrC nanoparticles could reduce the residual silicon and improve the microstructure integrity of composite. Furthermore, the variation of flexural strength and the flexural modulus showed an asynchronous trend with the increase of temperature. The flexural strength reached the maximum value at 1200 °C, but the highest elastic modulus was obtained at 800 °C. The strength increase was ascribed to the decrease of the thermally-induced residual stresses. The degradation of mechanical properties was observed at 1600 °C because of the microstructure deterioration and the formation of strongly bonded fiber–matrix interface. Therefore, it is concluded that the high temperature mechanical properties under vacuum were related to the consisting phase, the matrix microstructure, and the thermally-induced residual stresses.

Prediction of Thermal Residual Stress and Microstructure in Direct Laser Metal Deposition via a Coupled Finite Element and Multiphase Field Framework

Direct laser metal deposition (DLMD) is a modern powder-fed additive manufacturing process, which builds up complex objects layer by layer, providing a potential capacity to produce key structural components specifically for the aerospace industry. The printing process is of a multidisciplinary nature, and has gained increasing attention in the areas of engineering mechanics, material science, control engineering and many other related fields. The quality control of the printed part depends on a large number of process parameters. The aim of this work, therefore, is to develop a coupled finite element and multiphase field framework, that provides an effective way to understand the quantitative relationship between the process parameters, temperature history, thermally-induced residual stresses and microstructures in the DLMD process. More specifically, the established multiscale framework is able to sequentially couple the heat transfer, metal melting/solidification, and stress analysis to simulate the macroscopic temperature distribution, thermal residual stresses and dendrite growth and solute segregation in a thin wall structure made of a binary nickel-copper alloy. The latest simulation technologies are used to model the process of progressive material deposition as well as the movement of the laser beam. It has been found that the high intensity laser introduced in DLMD can produce a complex thermal history and a significant level of thermal residual stresses and distortion. Microstructure predictions demonstrate the location-dependent morphology evolution, e.g., the dendrite spacing and the degree of solute segregation, attributed to the spatially variant temperature history.

Simulation of buckling of internal features during selective laser sintering of metals

Additive manufacturing (AM) processes, such as Selective Laser Sintering (SLS), have enabled the fabrication of geometrically complicated designs. However, undesired distortions due to thermally-induced residual stresses may lead to loss of tolerance or failure of the part. One potential failure mode is buckling, particularly when realizing high aspect ratio features, like for infill, to minimize weight. In this paper, we address distortions and part failures due to buckling by using a finite element model to predict residual stress distributions and sintering induced distortions. Initially, we conduct a transient thermal simulation to determine the Heat Affected Zone (HAZ), which is then used in the thermomechanical simulation. In addition, we imposed perturbations on the mechanical mesh based on the buckling eigenmodes. Finally, a thermomechanical viscoplastic analysis was performed layer-by-layer to obtain the final residual stress state and subsequent distortions that occur after cooling down to ambient temperature. A model was used to describe the evolution of porosity due to laser sintering, and then a model of the effects of porosity on the viscoplastic constitutive properties of the sintered material was used in the thermomechanical simulation. Modeling results are compared against experimental specimens using a Durelli (aka, Theta) specimen geometry fabricated with a 3D Systems ProX 200 Selective Laser Sintering (SLS) machine. The geometry of the specimen represents an internal feature with a high aspect ratio that is prone to buckling, and the dimensions were modified based on the simulation results to confirm the ability of the modeling approach to provide accurate mitigation of buckling-induced distortions.

Microstructure, cracking behavior and control of Al–Fe–V–Si alloy produced by selective laser melting

Selective laser melting (SLM) technology based on atomized powder was used to fabricate Al–8.5Fe–1.3V–1.7Si (wt%) alloy parts. The microstructure and crack characterization of SLM samples fabricated at various conditions were presented. Results show that the cracks appear periodically along the building direction, initiate preferably at the outer edges of the as-built samples and propagated along the remelting border zone (RBZ) into deposited layers. Solid-phase cracking is proposed according to the fracture morphology. The thermal-induced residual stress during SLM combined with the precipitation of relatively large-sized AlmFe phase in the RBZ results in the formation of cracks. Enhancing scanning speed and hatch distance enable to reduce the cracking sensitivity. The crack-free Al–8.5Fe–1.3V–1.7Si parts can be fabricated at optimized parameters of laser power of 320 W, scanning speed of 1000 mm·s−1 and hatch distance of 0.10 mm along with proper laser pre-heating procedure. The samples built horizontally show good ultimate tensile properties of 454 MPa in average with the elongation of 7.2%.

An experimental–numerical investigation of heat distribution and stress field in single- and multi-track laser cladding by a high-power direct diode laser

Abstract High-power direct diode laser (HPDDL) cladding offers several advantages in the laser surface modification and repair of high-value parts. The wider beam and uniform energy distribution in the direct diode laser provide a smooth heating and cooling cycle during the cladding process. Subsequently, lower dimensional distortion and thermally-induced stress occur during the process. In this paper, temperature evolution and molten pool dimensions as well as stress-and-strain fields were studied by utilizing experimental and numerical methods. A three-dimensional (3D) transient uncoupled thermo-elastic–plastic model was developed to simulate a thermal process during the single- and multi-track laser cladding and the thermally-induced residual stress in the laser cladding. The effect of latent heat and phase transformations are considered in the thermal analysis. The numerical results were validated by experimentally-measured values, and the maximum prediction error was 3.5%. The experimental results were collected by in-situ monitoring techniques (e.g., thermocouples and a high-speed CCD camera). The level of residual stresses at the cladded surfaces were measured by an X-ray diffractometer. In addition, the effect of scanning speed on the thermal and stress evolution was quantitatively discussed.

Residual stresses in injection molded products

Injection molding is the most widely used processing technique for polymers. It offers several advantages over other processing conditions such as good surface finish, the ability to process complex parts without the need of secondary operations, and low cost for mass production. However, because of the complex deformation, and thermal and pressure histories that the polymer melt experiences during processing, residual stresses develop. These stresses act internally at room temperature and have the same effects on the material as externally applied stresses do, resulting in shrinkage and warpage of the product. In recent years, with the development and use of engineering plastics in an increasing number of applications, and with the tougher quality control policies in industries such as the automotive, the effects of residual stresses in product quality and performance have raised great interest. This review reports up-to-date advances in the field of residual stresses developments in polymers, with special attention given to injection molded products. Flow- and thermal-induced residual stresses are reported. Emphasis is given to the processing parameters that most influence residual stresses during injection molding as well as the effect of residual stresses not only on warpage but also on other material properties.

The Neutral Line Concept in Hot-Rolled Steel Cross-Sections

The present work deals with the effect of the thermally-induced residual stresses on the shape of a cross- section's neutral line for hot-rolled steel beams under combined loading conditions. In general, the neutral line of a beam cross-section is considered to be straight. In this study it is shown that, taking into account the existing thermal residual stresses, this line becomes a curve as far as the beam is subjected to pure bending or to combined loading that consists of a bending moment and an axial force.

Thermal-induced residual stresses affect the lifetime of zirconia–veneer crowns

ObjectivesThe purposes of this study were to investigate the effects of thermal residual stresses on the reliability and lifetime of zirconia–veneer crowns. MethodsOne hundred and twenty eight second upper premolar zirconia–veneer crowns were manufactured for testing the initial strength (n=64) and under cyclic fatigue (n=64). Zirconia copings (YZ Cubes, VITA Zahnfabrik, CTE: alphac=10.5ppm/°C) were milled using a Cerec3 InLab (Sirona) machine and sintered to a final thickness of 0.7mm. Sixty-four copings were sandblasted with 105μm alumina particles (15s, 3cm distance, 45° angle, 0.4MPa pressure) in order to trigger a tetragonalmonoclinic transformation and to produce a rough surface. The copings were veneered using two different porcelains (VM9, VITA Zahnfabrik, CTE: alphaVM9=9.1ppm/°C, Lava Ceram, 3M ESPE, CTE: alphaLava=10.2ppm/°C) so to result in crowns with either high thermal mismatch (+1.4ppm/°C with VM9) and low thermal mismatch (+0.3ppm/°C with Lava Ceram). The porcelains were applied by the same operator and fired (VITA Vacumat 4000) according to the firing schedules defined by the manufacturers to a final thickness of 1.4mm (total crown thickness=2.1mm, core/veneer ratio=0.5). After the last glaze firing the crowns were cooled following a fast (600°C/min) or a slow (30°C/min) cooling protocol. The glazed crowns were submitted to a sliding-motion (0.7mm lateral movement) cyclic fatigue in a chewing simulator (SD Mechatronik) under 20kg (∼200N load) weight until failure (chipping) (n=16). The other half of the crowns were subjected to a compressive loading test in an universal testing machine (Instron model 4240) until failure at a cross-head speed of 0.75mm/min (n=16). The failure probability for initial strength and cyclic fatigue was performed using a Weibull distribution approach at a scale factor of n=16. ResultsThe compressive strength test showed a low sensitivity to detect reliability variations regarding thermal stresses created within the veneer layer of tested crowns. For cyclic fatigue, slow cooling resulted in statistically higher cycles to failure only for the crowns that presented a high thermal mismatch between core and veneer (VM9 group). Comparisons between veneers with high or low thermal mismatches showed statistically higher sigma0 for Lava Ceram-veneered crowns only when the groups were fast-cooled. SignificanceMinimizing the thermal residual stresses within the veneer through the use of a veneer with a closer CTE to the zirconia delays the failure of zirconia–veneer crowns. Slow-cooling increases the lifetime of crowns presenting large differences in CTE between the zirconia core and the veneering porcelain.

RESIDUAL STRESS MEASUREMENTS AND STRUCTURAL INTEGRITY IMPLICATIONS FOR SELECTIVE LASER MELTED TI-6AL-4V

Selective laser melting (SLM) of Ti-6Al-4V has significant potential in the aerospace and biotechnology industries. SLM employs a focused laser beam to melt successive layers of metallic powder into complex components. This process can result in the generation of high thermally-induced residual stresses. These residual stresses, together with micro-flaws/ pores from the inherent fabrication process, may lead to premature fatigue crack initiation and propagation at relatively low cyclic stresses. The hole-drilling strain gauge method was used to evaluate residual stresses within SLM Ti-6Al-4V specimens, with the intention of understanding the associated mechanisms for the successful application of SLM Ti-6Al-4V in industry.

Numerical Analysis on Cooling Process of Monocrystal Silicon Rod Manufactured with Czochralski Method

A numerical analysis was performed to investigate the temperature distribution and thermal stress field in monocrystal silicon rod in the cooling process of manufactured with Czochralski (CZ) method. The thermally-induced residual stress fields of silicon rod under different length of cool-down time conditions were obtained as well as temperature fields, respectively. All simulations were finished by using ANSYS finite element code. It showed that, maximum thermal stress was mainly appeared on rod surface, the influence of length of cool-down time on it was not remarkable, the magnitude of it was far below the critical strength of silicon throughout.

Microlevel manufacturing process simulation of carbon fiber/epoxy composites to analyze the effect of chemical and thermal induced residual stresses

A micromechanical implicit finite element analysis using Samcef/Mecano was performed to analyze the effect of process-induced deformations and stresses on a unidirectional carbon fiber–epoxy composite material (G1157/RTM6). During the manufacturing process, chemical and thermal shrinkage deformations occur and lead to internal stresses. In this article, several effects on the level of stress on the microscale will be discussed, which address the nonlinear behavior of the polymer matrix material. A parametric study was done on the influence of these effects on residual stresses including temperature dependency of the young’s modulus, thermal expansion coefficient, nonlinear thermomechanical stress–strain behavior, microyielding, microdegradation, and viscoelasticity. Several experiments have been carried out to investigate the thermomechanical behavior of the matrix material and to derivate constitutive equations. The derived equations and the discussed effects are integrated into an analysis model of a squared unit cell and used to perform a coupled curing thermomechanical simulation. As a result, the development of process-induced stresses is presented with the integration of nonlinear local material effects. Assessment of these effects is one of the key aspects for interpretation of process-induced stresses on the macroscale.

Numerical Analysis of Thermally-Induced Residual Stresses in Beryllium Caused by BeO

A numerical analysis was performed to investigate the thermally-induced residual stress caused by the thermal expansion mismatch between Be and BeO. Models were constructed according to the real situation that the BeO particles embedded in grains or distributed at the grain boundaries, where the temperature-dependent materials properties, particle volume fraction and size and interparticle distance were taken into account. In simulation, it supposes particles inside grain no interacting with others, particles along the grain boundary being a period distribution. Be is modeled as elastic and elastic-plastic material with bilinear kinematic hardening model. BeO is modeled as isotropic and linear elastic. All simulations are performed by using ANSYS finite element code. Results show that the size, location and the volume fraction of particles influence on the residual stress (strain) to different extent during cooling process.