Thermal Residual Strain Research Articles

A fast numerical method of introducing the strengthening effect of residual stress and strain to tensile behavior of metal matrix composites

Thermal residual stress and strain (TRSS) in particle reinforced metal matrix composites (PRMMCs) are believed to cause strengthening effects, according to previous studies. Here, the representative volume element (RVE) based computational homogenization technique was used to study the tensile deformation of PRMMCs with different particle aspect ratios (AR). The influence of TRSS was assessed quantitatively via comparing simulations with or without the cooling process. It was found that the strengthening effect of TRSS was affected by the particle AR. With the average strengthening effect of TRSS, a fast method of introducing the strengthening effect of TRSS to the tensile behavior of PRMMCs was developed. The new method has reduced the computational cost by a factor 2. The effect of TRSS on continuous fiber-reinforced metal matrix composite was found to have a softening-effect during the entire tensile deformation process because of the pre-yield effect caused by the cooling process.

Mechanical Behavior of Impregnated REBCO Pancake Winding Based on Electromagnetic-Thermoelastic Analysis

In this study, the mechanical behavior of an impregnated single pancake wound with a REBCO coated conductor is analyzed in magnetic field after its cooling through finite element (FE) modeling. A two-dimensional axisymmetric FE model with averaged material properties of the impregnated winding is developed. First, the thermal residual stress and deformation accumulated during cooling from 300 K to 4.2 K are analyzed. Using the thermal residual stresses and strains as initial conditions, the mechanical behavior of the impregnated winding under the self-field and background field are subsequently studied. Finally, the contribution of the thermal mismatch stress as well as the Lorentz force under the self-field and background field to the radial stress of the impregnated pancake winding is discussed, and the risk of delamination failure under each situation is evaluated. The results show that the radial stress due to the thermal mismatch increases with the decrease of cooling temperature. As the transport current increases, the radial stress decreases under the self-field, but increases under the background field. The discussion indicates that there is the potential risk for delamination failure during cooling, and the risk increases with the decrease of temperature. If delamination does not appear after cooling, the winding will not be damaged owing to interfacial debonding under self-field. However, the risk of delamination failure increases upon increasing the transport current under a strong background field.

A Three Dimensional Unit Cell Model for the Analysis of Thermal Residual Stresses in Polymer Composites Reinforced with Wavy Carbon Nanotubes

ABSTRACTThis paper presents a numerical approach to predict the thermal residual stresses in polymer nanocomposites reinforced with a periodic array of wavy carbon nanotubes. A three dimensional unit cell model is established to accurately account for the waviness of the nanotube. Periodic boundary conditions are determined for the unit cell with a pair of curved surfaces. Appropriate methods to evaluate the macroscopic stresses and strains are also determined for the unit cell model in which the interior pores of the nanotubes are explicitly included. It is demonstrated that the macroscopic behavior of the nanocomposites is orthotropic due to the symmetries manifested. By employing material properties of the two constituents, the thermal residual stresses and strains induced by high temperature curing and cooling-down are predicted for an epoxy/wavy-nanotube composite. It is also demonstrated that the curing process tends to increase the waviness of the nanotube and the waviness has a significant influence on the distribution of the microscopic residual stresses.

Parametric investigation on the thermal aspects of superconducting REBCO tapes used in CORC cables

The primary aim of this study is to understand how the thermally induced strain varies with change in thickness of REBCO tapes. During the production stage of REBCO tapes, a residual thermal strain is induced in it due to cool down from 1020 K to 77 K. The 4 mm long and 0.091 mm thick REBCO tape cools down from 1020 K to a 0.17% residual compressive strain at room temperature and cools down to a 0.242% residual compressive strain at liquid nitrogen temperature. But these values are dependent upon the thickness of other elements in the REBCO tape. A mathematical model for the system is developed and validated using experimental data. The model is then subjected to different practical conditions and its thermal behaviour is evaluated. The performance of the superconductor is closely monitored and the degradation is determined for each case. The study has given more information on how the thermally induced strain differs with changes in thickness of REBCO tapes. The results obtained are expected to make modifications in the current production process for REBCO tapes and in its eventual usage.

Multi-objective particle swarm optimisation of multilayer functionally graded coating systems for improved interfacial delamination resistance

In this paper a multilayer coating system was considered for a 316 L stainless steel substrate with potential application for hydrogen storage. The coating system was comprised of a 316 L stainless steel/Al2O3 functionally graded (FG) layer and a SiC top coat. The composition gradation and thicknesses of the FG layer and SiC top coat were considered as parameters to be optimized for higher edge interfacial delamination resistance within the system. A novel method of delamination energy variation was first used for finite element analysis (FEA) of the system and the best set of parameters were defined as well as an interfacial delamination criterion (maximum stable edge delamination crack length in the system). Analytical solutions of thermal residual stress, strain and strain energy density were also studied for the system. Two new multi-objective functions were derived based on the analytical equations and further investigated to maximize interfacial delamination resistance of the system using multi-objective particle swarm optimisation (MOPSO). The optimized conditions achieved by different methods were finally compared and concluded to be in good agreement. Overall, the use of the new objective functions for MOPSO, combined with FEA, increased the maximum stable delamination crack length from 7 μm (obtained by a thermal residual stress criterion used by previous researchers) to 50 μm (using the new method). Therefore, FEA based on energy variation and MOPSO with the new objective functions were found to be applicable for optimisation with respect to interfacial delamination resistance.

Numerical and Experimental Investigation of Aluminum/CFRP Hybrid Tubes with Rubber-like Interlayer

In the automotive, aerospace, printing, and sports industries, the development of hybrid CFRP-metal components is becoming increasingly important and used. The coupling of metal with CFRP, in axial symmetric components, results in reduced production costs and an increase in mechanical properties such as bending, torsional stiffness, mass reduction, and critical speed, when compared to the single material-built ones. The challenge for engineers is to design hybrid co-cured tubes with external metal layers, which avoid possible detachments and delaminations due to the mismatching coefficients of thermal expansion of the two materials. In this work, residual thermal stresses and strain have been studied with numerical models based on Finite Element Method (FEM) and compared with experimental tests. The FEM model allowed for the investigation of the influence of length, diameters, thickness and interface layer material on residual thermal stress peaks near the free edges zone. To reduce the risk of premature failure,the interleaving of a rubber-like layer is proposed and experimentally validated.

Stress, strain and electromechanical analyses of (RE)Ba2Cu3Ox conductors using three-dimensional/two-dimensional mixed-dimensional modeling: fabrication, cooling and tensile behavior

High temperature superconducting (HTS) conductors, represented by Rare Earth-Barium-Copper-Oxide (REBCO) conductors, are promising for high energy and high field superconducting applications. In practical applications, however, the HTS conductors experience different stresses and strains, including residual stresses due to thermal mismatch and tensile stresses due to Lorentz forces, resulting in some circumstances to a reduction in the load-carrying capacity as well as the risk of degradation in conductor critical current. In this study a mixed-dimensional high-aspect-ratio laminated composite finite element model for REBCO conductor is developed for stress and strain analyses in the processes of fabricating and cooling, as well as tensile testing. The model includes all the major constituent layers of a typical REBCO conductor and is experimentally validated. First, the thermal residual stresses and strains accumulated during the fabrication and cooling processes are analyzed by a multi-step modeling method that emulates the manufacturing process. Then, with the residual stresses and strains as initial stresses and strains, the mechanical behavior under a tensile load is studied. Lastly, a phenomenological critical current-strain model based on the Ekin power-law formula and the Weibull distribution function is combined with the mixed-dimensional conductor model to predict the strain dependence behavior of critical current in the reversible and irreversible degradation strain ranges. Simulation results show that the multi-step modeling is an effective method for stress and strain analyses of REBCO conductors during the fabrication and cooling processes and under and tensile loads. Compressive thermal residual stress generated on the REBCO layer during fabrication and cooling strongly affects the subsequent mechanical and current-carrying properties. Stress–strain curves generated by tensile loads are analyzed and experimentally validated at both the conductor and constituent-layer levels. Simulation results for the strain dependence of critical current are in good agreement with experiment data in both the reversible and irreversible degradation stages.

Residual Thermal Strain Distribution Measurement of Underfills in Flip Chip Electronic Packages by an Inverse Approach Based on the Sampling Moir\xe9 Method

Residual deformation evaluation of underfill (UF) materials in flip chips is crucial to improve the reliability of electronic packages. In this study, we propose to evaluate the residual thermal strain distributions using an inverse method based on the sampling moiré technique. Even if a grid pattern is fabricated on the specimen at room temperature, the residual strain distributions at an arbitrary temperature relative to the specimen formation temperature can be successfully calculated. The residual strain distributions relative to the free contraction state at an arbitrary temperature can also be measured when the coefficient of thermal expansion is available. A thermal chamber for flip chips was designed under a laser scanning microscope. Using the proposed method, the normal, shear and principal internal strain distributions and deformation characteristics of two kinds of UFs in flip chips were investigated relative to 150 °C. The strains of the UF with low glass transition temperature (UF-A) concentrate near the die material, especially at the die corner, while the strain concentration of the underfill with high glass transition temperature (UF-B) mainly occurs at the die corner and the buffer layer. The maximum principal strain of UF-A is greater than that of UF-B around the die corner. The residual maximum principal strain distributions relative to the free contraction state at 25 °C were compared with the simulation results by the finite element method. The residual strain distribution trends from experiments are consistent with those from simulations.

A level-set based continuous scanning path optimization method for reducing residual stress and deformation in metal additive manufacturing

Thermal residual stress and distortion inherent in metal melting and solidification process is the main cause of build failure in metal additive manufacturing (AM) techniques such as laser powder bed fusion and directed energy deposition. To ensure build quality against residual stress/distortion, it is desirable to tailor the scanning path for a given geometry that needs to be built. Since the local deformation introduced by the moving heat source is anisotropic due to non-uniform heat transfer and mechanical constraints, the scanning path can affect residual stress within a part significantly. Aiming at thermal residual stress/distortion mitigation, this paper presents a novel level set-based scanning path optimization method. The method is developed to enable layer-wise continuous scanning path optimization for geometrically well-defined parts. To make the optimization efficient, a fast process simulation method called the inherent strain method is employed to simulate the thermal residual strain. Full sensitivity analysis for the formulated compliance- and stress-minimization problems is provided, where a novel strategy called the adaptive level set adjustment (ALSA) is proposed to remedy the deficiency of ignoring the non-implementable sensitivity terms. The effectiveness of the proposed continuous scanning path optimization method and ALSA strategy has been proved by a few numerical examples. Finally, the concurrent design scenario for simultaneous scanning path and structural optimization is investigated to demonstrate the further residual stress reduction.

The determination of thermal residual stresses in unidirectional and cross-ply titanium matrix composites using an etch removal method

Recent work has shown that a simple rule-of-mixtures approach may be used to predict the stress–strain behaviour of a cross-ply metal matrix composite laminate. However, the low-strain behaviour was not predicted accurately, probably because thermal residual stresses are obviously not included in such an approach. To increase the understanding of the limitations of the rule-of-mixtures approach for predicting the stress–strain response, the residual strain-state of the fibre reinforcement has been determined using an etching technique (henceforth referred to as the ‘total etch removal method’), and results have been compared both with finite element modelling and with thermal residual strain measurements derived from stress–strain curves. The results show that the residual strain distribution in a cross-ply composite may be more complex than previously thought, with the fibres in internal 0° plies having considerably higher thermal residual strains than fibres in external plies. The results confirm that the rule-of-mixtures approximation can be used, with some reservations with regard to the low-strain behaviour.

Dilation Behavior of Thermal Spray Coatings

The thermal expansion of a thermally sprayed coating material is an important design-relevant property from both processing and application service points of view. High thermal stresses and residual strains can arise during deposition, and thermal exposure in service. The linkage to process conditions which can impact both physical and chemical attributes of the microstructure and consequently its expansion behavior is of great importance. The observed dilation response of various coatings is discussed based on the processing effects that induce differences in microstructural features and the impact of residual strain and annealing of defects on the dilation behavior during first thermal exposure. The coefficient of thermal expansion (CTE) of coatings was found to approach the bulk when the material is not sensitive to oxidation in-flight. For those materials sensitive to oxidation, mathematical models used to describe effective properties of composite materials were adopted to describe the CTE property. A large irreversible dilation change was found in the first heating cycle due to defect annealing (referred to as thermal shakedown). Several reasons are hypothesized for the magnitude of such dilation change. Together, the paper presents a comprehensive analysis of thermal expansion behavior of a diversity of thermal spray processed materials.

On thermal strains and residual stresses in the linear theory of anti‐sandwiches

AbstractThe current study aims to formulate the behaviour of anti‐sandwiches that considers residual stresses and thermal strains by means of a layer‐wise approach. To this end, the constitutive equations of classical linear elasticity are extended to form the Duhamel‐Neumann equations. The direct approach is adopted to project the three‐dimensional problem onto two‐dimensional surfaces, i.e., each layer of the anti‐sandwich is modelled as a single surface that represents the overall behaviour of the layer. The formulation of the problem begins with the decoupling of deformation into independent membrane, bending, twisting and transverse shear modes. The infinitesimal deformation measures are set up on the kinematics of the problem and related to the corresponding kinetic measures via the proposed stiffness relations. The resulting boundary value problem is converted into the equivalent weak form by means of a variational approach. The presented set of equations can be solved inexpensively using various computational approaches such as the finite element method.

Failure mode analysis of CFRP-SPCC hybrid thin laminates under axial loading for structural applications: Experimental research on strain performance

The failure mode behavior of hybrid thin laminates consisting of Carbon Fiber Reinforced Plastic and Steel Plate Cold Commercial (CFRP-SPCC) in term of quasi-static tensile test was observed. The different fundamental failure mechanisms of fiber breakage, layer delamination, and matrix damage are discussed. The results from the experiment are compared with Finite Element Analysis (FEA) using Hashin failure criterion, and considered for more in-depth analysis using surface morphology of the [SPCC/±45/0]S specimen. The experimental results show that hybrid laminates can delay the premature fiber breakage and delamination of the laminates as well as increase the strain at the maximum stress up to 16%. The numerical model using FEA software showed Residual Thermal Compressive (RTC) stress and strain had a significant effect on the increased of strain performance in hybrid laminates due to the difference of Coefficient of Thermal Expansion (CTE) value between SPCC and CFRP.

Measurements of the Strain Dependence of Critical Current of Commercial REBCO Tapes at 15 T Between 4.2 and 40 K for High Field Magnets

Author(s): Pierro, F; Delgado, M; Chiesa, L; Wang, X; Prestemon, SO | Abstract: Interest for high magnetic fields (g16 T) for applications in high energy physics (HEP) and fusion machines, requires the development of high current cables capable to withstand the large forces, mechanical and electromagnetic, experienced during manufacturing and operations. The critical current (Ic) of REBCO tapes depends on strain, magnetic fields, and operational temperatures. Understanding how these parameters affect the Ic of the conductor will be critical to develop robust high-current REBCO cables. However, there are limited reports on the strain dependence of Ic, in particular at high fields and elevated temperatures relevant for future high-field compact fusion reactor magnets. We present Ic of commercial REBCO tapes measured as a function of compressive and tensile strain (between-0.6% and +0.65%) at high magnetic fields (12 and 15 T) and different temperatures (within 4.2-40 K). Results at 4.2 and 20 K showed less than 5% reduction in the normalized Ic at high strain, while a stronger strain dependence was observed at 40 K. Samples tested at 12 T and 4.2 K showed similar strain dependence as 15 T and 4.2 K. In all tested conditions, the tape experienced reversible Ic reduction in both tension and compression. Finite element analysis was used to predict the residual thermal strain accumulated in the REBCO layer prior of testing to account for the effect of the cooldown. A method was also developed to account for the current sharing observed between the sample and the sample holder during the ramp of the current. Our results provide useful input for the development of high-field fusion and HEP magnets using REBCO conductors.

The strain performance of thin CFRP-SPCC hybrid laminates for automobile structures

In this study, the strain performances of CFRP-SPCC hybrid laminates are investigated. The quasi-static tensile test and classical lamination theory (CLT) was used and compared to evaluate strain performance of hybrid laminates consisting of 0°, 45°, −45°, and 90° plies and SPCC plate. The experimental results show a maximum strain of 1.85% at the maximum stress for [0]4 and 2.15% for [SPCC/±45/0]S hybrid laminates. The hybrid laminates have shown that adding SPCC to CFRP laminates can increase the performance of the laminates by delaying the failure for more than 16% in terms of strain. The different failure modes of the laminates after tests are observed and evaluated considering the residual thermal strains and stresses.

Prediction for progression of transverse cracking in CFRP cross-ply laminates using Monte Carlo method

This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.

The effect of stress-aging on dimensional stability behavior of Al-Cu-Mg alloy

The stress-aging method is proposed to improve the dimensional stability of Al-Cu-Mg (2024 aluminum) alloy. Both the reduction of residual stress and the acceleration of precipitates are investigated during the stress-aging process. It is observed that some S′ particles precipitate in the alloy during stress-aging. With the external stress increase to 100 MPa, the residual stress and thermal strain (ɛc) decrease, while the micro-yield strength increases significantly. This is attributed to that the dislocations are effectively pinned by the uniformly distributed precipitates and the stored elastic energy diminishes remarkably, which leads to a considerable improvement of the dimensional stability of 2024 aluminum alloy. However, when further increases the external stress to 150 MPa, due to the coarsened precipitates, the residual stress and thermal strain increase, while the micro-yield strength decreases slightly.

Thermal residual solutions of beams, plates and shells due to laminated object manufacturing with gradient cooling

Laminated object manufacturing (LOM) results in thermal residual stresses and deformations due to its material mismatch among layers and gradient cooling. The manufacturing and cooling processes in a laminated workpiece are decomposed into many turns. Through-thickness cooling gradients are considered in each layer forming turn. The thermal residual strains in each turn are deduced. The total thermal residual stresses are obtained by composing the strains in all turns. The workpieces with geometries of a beam, plate and shell are considered. For a beam or plate, the analytical solutions of the stresses and deformations in the axial and transverse directions are deduced separately and then synthesized to the total solutions. One-dimensional beams and two-dimensional plates have very similar solutions. For a symmetrical hollow cylinder or sphere, the analytical solutions of thermal residual stresses with through-thickness cooling gradients are also formulated. The numerical examples show that the assumption of synchronous cooling results in big errors and cooling gradients also induce thermal residual stresses and deformations. Four gradient cooling models are summarized according to various LOM manufacturing techniques and the thermal residual level is proportional to the cooling gradient. Processing sequence in functional gradient materials has a strong impact on thermal residual level.

Residual Stresses Introduced to Composite Structures due to the Cure Regime: Effect of Environment Temperature and Moisture

Material behaviour of structural components is very important to understand. In fibre reinforced polymer composite materials, this is more difficult in comparison to isotropic materials as they are made up of two constituents: the fibre and the matrix. For aerospace composite materials, the matrix is usually an epoxy resin that cures at a high temperature. This curing regime is known to introduce residual stresses to the composite material as it cools from the high cure temperature. However, how to consider these residual stresses in a structural analysis is still widely debated. In this paper, the authors investigated the offset of thermal residual strains introduced by the cure regime by the swelling of the composite when exposed to moisture.

Initial thermal stress and strain effects on thermal mechanical stability of through silicon via

This paper is concerned with the thermal mechanical stability of 3D TSV with initial thermal stress and deformation during working stage. Different from the previous results, integrated circuits (IC) packaging and fabricating process (PFP) is considered to obtain the initial thermal stress and strain for working stage. During the PFP of IC, the through silicon via (TSV) may go through several different processes, such as, making redistribution layer (RDL), reflow soldering, and filling under-fill. Since more than 70% of the PFP brings high thermal load, plastic deformation on TSV Cu is inevitable during PFP. The accumulation of the plastic deformation leads to thermal residual stress and strain at the beginning of working cycling stage. The thermal mechanical reliability and mechanism of the TSV were investigated by finite element (FE) method. The influence of thermal residual stress on the IC fatigue life was studied by comparing neglecting PFP (NPP) model with considering PFP (CPP) model. With different forms of plastic deformation and effective plastic strain accumulation during PFP, the lifetime is shortened at the middle part and prolonged in the TSV Cu interfacial line. The precision of evaluation and prediction the IC reliability was improved by CPP greatly, e.g. the minimal fatigue life of the TSV unit is 75cycles for NPP and 118cycles for CPP. With full consideration of the thermal mechanical mechanism related to the IC PFP, the fatigue life will be prolonged.