Thermal Residual Strain Research Articles

Thermal stress induced by the adhesion topology of a semiconductor integrated circuit package

In the semiconductor integrated circuit (IC) package, the top surface of the silicon chip is directly attached to the lead frame by a double-sided adhesive layer. Under the functional operation, the IC package has been known to encounter such thermomechanical failure as delamination. This failure is due to the thermal residual strain and stress of the adhesive surface on the silicon chip in the curing-cooling process. The induced thermal effects in the curing process affect the fatigue life of the IC package. Thus, it is necessary to reduce the thermal stress induced on the silicon chip. In this paper, to reduce the surface failure and improve the durability of the silicon chip, the adhesive topologies and thermal stresses on the silicon chip at curing temperature are studied by finite element analysis (FEA).

Strain monitoring of braided composites by using embedded fiber-optic strain sensors

Recently, fiber optic strain sensors have been applied to internal strain and damage monitoring of composites because of their small size, light weight and flexibility. Braided fiber reinforced plastics (FRP) are compatible with fiber optic sensors because optical fibers can be integrated directly and easily into fabrics. In the present paper, the strain monitoring of braided glass fiber reinforced plastics (GFRP) was conducted by using embedded fiber Bragg grating (FBG) and extrinsic Fabry–Perot interferometric (EFPI) sensors during the cure process, tensile tests and fatigue tests. From the experimental results of cure monitoring, it was found that both sensors can be used only for monitoring of thermal residual strain during cooling process. From the results of tensile tests, it was found that both sensors could measure strain correctly until damage initiation of braided GFRP. It also appeared that FBG sensors could monitor damage to FRP by observing the reflected spectral shape. From the fatigue tests, it appeared that the strain measured by embedded FBG sensors was affected by fatigue damage. Therefore, it is concluded that internal strain monitoring of braided FRP using fiber optic strain sensors is very useful for cure and health monitoring.

Application of a First Invariant Strain Criterion for Matrix Failure in Composite Materials

This paper reports an application of the strain invariant failure theory (SIFT) proposed by Gosse to through-thickness failure of composite structures [Gosse, J.H. and Christensen, S. (2001). Strain Invariant Failure Criteria for Polymers in Composite Materials, AIAA-2001-1184]. It includes global 3D finite element analysis on a ply-by-ply basis and the determination of amplification factors for strains in the intrafiber resin and the calculation of thermal residual strain due to manufacturing for intrafiber resin using micromechanical models. The new procedure has been applied to matrix failures for one type of curved beam, two types of I-beam and two types of T-cleat structures. The resulting predictions of the failure loads for both the I-beams and the T-cleats follow experimental trends. The limiting value of the first invariant strain for failure of the resin in the unidirectional tape is 17,000–20,000 ", and in the bidirectional fabric is 26,000–27,000 ".

Estimation of the coefficient of thermal expansion of Bi2223 at low temperature

The evaluation of the coefficient of thermal expansion (CTE) of each constituent in Bi2223 composite tape is essential since the thermal residual strain exerted on Bi2223 during cooling from annealing temperature gives the important effect on the strain endurance of critical current (Ic). In the present study, the thermal expansion of Ag, Ag alloy and the composite tapes was measured during heating from 7 K to RT by means of Nyilas type extensometers. Mechanical properties of Ag and Ag alloy such as Young's modulus and yield stress were measured at RT and 7 K because they are also necessary for the analysis based on the rule of mixture. Comparing the measured thermal expansion of Ag tape with the reference data of Ag bulk, it is confirmed that the present technique is useful, even for the thin tape. From the analysis taking yield of the Ag into account, CTE of Bi2223 in the multifilamentary tapes were determined. It was found that CTE of Bi2223 in the present study locates between the reported data of αab and αc, which represent the CTE parallel to the ab-plane and c-axis. These are the first results on CTE measurement of Bi2223 at low temperature by the indirect method.

Microscopic fracture of filaments and its relation to the critical current under bending deformation in (Bi,Pb)2Sr2Ca2Cu3O10 composite superconducting tapes

The strain dependence of the critical current, Ic, of (Bi,Pb)2Sr2Ca2Cu3O10 (Bi2223)/Ag/Ag–Mg composite superconducting tapes has been studied both experimentally and analytically under bending deformation. Tests have been carried out for one type of tape used in the VAMAS bending round-robin programme. The complex stress–strain behaviour of each component was first analysed in tension. This was done by comparing the stress–strain curves of composite tapes with those of Ag and Ag–Mg alloy tapes. Here, the plastic deformation (work hardening) of Ag and Ag–Mg alloy, and the thermal residual strain due to the manufacturing process were taken into account. The fracture strain of Bi2223 filaments was inversely determined as 0.08% to meet the global tensile stress–strain curve of the composite tape. The calculated stress–strain curves finally agreed well with the experimental results when the as-supplied bending strain was taken into account. Then, the analysis was modified to fit the bending deformation. Here, the movement of the neutral axis due to the non-symmetric and elastic–plastic stress–strain curves of the components and their Bauschinger effect were taken into account. The relative decrease of Ic with the increase in the Bi2223 tape curvature was calculated from the volume fraction of the broken filaments. The calculated Ic agreed well with the experimental results when the movement of the neutral axis and the Bauschinger effect were taken into account. Microscopic observation of the spatial distribution of the filament fracture indicated that the damage occurred at the outermost layer on the tensile side when the curvature was small, and then the damage front shifted to the inside layers. The observed fracture behaviour of the Bi2223 filament agreed well with the estimated location based on the above analysis.

Finite element evaluation of hydrogen solubility enhancements due to thermal residual stresses in palladium–alumina composites

Residual tensile stresses in materials result in hydrogen solubility enhancements. The residual thermal stresses and strains developed in Pd–alumina composites on cooling from several different high temperatures have been modeled by the finite element method (FEM). Two cases (alumina forming the inner core in the first case and Pd in the second case) were considered for modeling spherical alumina precipitates distributed in a spherical Pd matrix. The advantage of utilizing the FEM model is highlighted, namely the variation of stress components in different states of stress can be determined as a function of position in the composite. The FEM model provides insights into the locations where hydrogen will segregate. The stresses evaluated have also been related to hydrogen solubility enhancements.

Neutron Diffraction Study of Thermal Residual Strain in Three Layered Materials Made by Self-propagating High-temperature Synthesis

The thermal residual strain in the three layered materials, [WC-10mass%Ni]-[Ni]-[WC-10mass%Ni], [WC-10mass%Ni]-[SUS304(plate)]-[WC-10mass%Ni] and [WC-10mass%Ni]-[Ni(plate)]-[WC-10mass%Ni], has been investigated by neutron diffraction measurement. They were made by self-propagating high-temperature synthesis. Original materials of composite [WC-10mass%Ni] are powders of W, C and Ni, and those of the middle layers are the powders of Ni, a plate of SUS304 and a plate of Ni. The samples were 40mm in diameter and about 4mm in thickness of each layer. The result of the measurement shows that the middle layer made from powders of Ni has no strain, which suggests that it shrinks from high temperature freely from the existence of both side layers. On the other hand, the middle layer made from a plate material experiences complex stress according to each position and to each direction of the sample, which suggests that it shrinks from high temperature in a state of tight binding on both side layers. The Ni region in the composite material, [WC-10mass%Ni], has a large tensile strain of 0.6 to 1.0%, whereas WC region has a negligibly small compressive strain. In this case, the Ni region shrinks under the hard connection with the WC region, of which the thermal expansion coefficient is relatively small.

Ferro- and piezoelectric properties of Bi4−xPrxTi3O12 polycrystalline thick films with Ps-vector orientation

ABSTRACTTo reveal the complete performance of intrinsic ferroelectriciy-related properties in single crystalline bismuth-layer-structured displacive ferroelectrics in film form on Si, the crucial roles of both orientation control technology by lattice matching from the atomic arrangement of substrate layer and configuration of the volume fraction of 90°-domain during cooling process were demonstrated. 1.2 μm-thick and Pr3+-substituted Bi4-xPrxTi3O12 (BPT, x =0.0, 0.3, 0.5, 0.7) films were grown on Ir(111)/Ti/SiO2/Si(001) substrates by chemical solution deposition (CSD) method with preferred orientation along the major component of Ps vector. BPT film of x =0.3 exhibited superb ferroelectric properties of remanent polarization 2Pr=92 μC/cm2, saturation polarization Psat=50 μC/cm2, and coercive field 2Ec=184 kV/cm. The film also showed uniform piezoelectric response with an effective piezoelectric coefficient of AFM-d33=36 pm/V. During the decomposition of precursor solutions, IrO2 layers were formed at the surface of Ir layers and promoted a/b-axes orientation. During the cooling process after grain growth, in addition, the differential thermal expansion and residual strain between film and substrate introduced bidirectional lateral stress into BPT film and might eliminate the 90°-domain walls dividing a-and b-domains through the relaxation by domain formation at the Curie temperature TC. Consequently the polar-axis orientation was distinctively grown along the film normal and the conjugate non-polar-axis was grown in-plane.

Measurements of material properties using differential capacitive strain sensors

This paper describes a laterally deflecting micromachined device that offers high sensitivity and wide dynamic range to electronically monitor the thermal expansion coefficient, tensile and compressive residual strain and Young's modulus of microstructural materials, as well as the temperature dependence of these properties. The device uses sidewall capacitance between interdigitated tines to sense displacement caused by the release of residual stress in a bent-beam suspension. Electrostatic force is used to obtain load-deflection profiles. The suspensions and tines are arranged such that output is a differential readout, immune to common mode parasitic capacitance. Analytical and numerical modeling results are presented and the device concept is verified by three different fabrication approaches using polysilicon and nickel as structural materials. Measured values of residual strain, thermal expansion and Young's modulus are very consistent with measurements taken by other approaches and those reported previously. For example, the residual strain in certain electrodeposited Ni structures was tracked from 68.5 microstrain at 23/spl deg/C to -420 microstrain at 130/spl deg/C, providing an expansion coefficient of 8.2 ppm/K; the best fit Young's modulus provided by the device was 115 GPa.

Behavior of Metallic Samples Subjected to External Stresses during Heating-Cooling Cycles

Measurements performed with a high sensitivity dilatometer showed that metallic samples subjected to heating-cooling cycles undergo a permanent change in their length. The ratio between the end-of-cycle length and the initial one, named Thermal Residual Strain (TRS), changes from positive to negative values by increasing the maximum temperature of the cycle. This dependence of TRS on cycle maximum temperature is similar for all the examined metals (aluminum, copper, lead, iron and gold). In this contribution we will show the preliminary experimental results on behavior of TRS in aluminum samples when subjected to an external stress acting in direction opposite to the thermal dilation. By increasing the stress, the temperature, at which the positive residual strain is maximum, becomes lower and lower until the positive TRS disappears. If the stress intensity decreases this temperature rises and the positive TRS behavior becomes a flat curve without a marked maximum.

Residual Thermal Phase Stresses in α-γ Fe-Cr-Ni Alloys Measured by a Neutron Diffraction Time-of-Flight Method

Residual thermal phase elastic strains in rod specimens and powders with particle size from 150 to 250 \\micron of α-γ Fe–Cr–Ni alloys quenched from 1273 to 273 K, were measured by means of a high-resolution neutron powder diffractometer using a time-of-flight (TOF) method. Diffraction patterns were analyzed by the Rietveld method and the single-peak method. Residual thermal phase strains obtained in the rod specimens or the powders from the both methods are positive, i.e., tensile, for austenite (γ) phase and negative for ferrite (α) phase, being consistent with the prediction from the difference in thermal expansion coefficients of the constituent phases. The Rietveld analysis combined with the TOF method is considered to give the most reliable results of the average thermal phase strain. The results by the single-peak analysis suggest that thermal phase strain shows [hkl] dependence; the absolute value of thermal phase strain is decreased with increasing of the Young modulus along the [hkl] direction.

Thermal Residual Stresses in Bonded Repairs

The number of ageing aircraft is increasing and will further increase considerably in the near future. The control of damage by inspection and repair becomes therefore more and more important. The bonded repair method proved to be a cost-effective way to repair damage. However, this method has some disadvantages. One of them is the introduction of thermal residual stresses in the repair, due to the mismatch in coefficients of thermal expansion between the skin material and the repair material. Two analytical models are available to determine these residual stresses in the repairs, i.e., the Wang–Rose model and the Van Barneveld–Fredell model. A new computer program CalcuRep2000 [1] is being developed. This computer program will be used to calculate the stresses in bonded repairs, and is developed by the US Air Force in co-operation with the faculty of Aerospace Engineering of Delft University of Technology in The Netherlands. For this program an analytical model, which is able to calculate the thermal stresses in a bonded repair accurately, is essential. This paper describes how the most adequate analytical model was identified by comparison with Finite Element (FE) analysis. Two repair configurations were distinguished: The test specimen, i.e., bonded repair specimens used for fatigue tests in laboratories, and the in-field specimen, i.e., a realistic repair. The difference between both repair configurations is that a test specimen is free to expand during curing while in a realistic repair configuration expansion is partly prevented by the cooler surroundings of the heated area. The analytical model of Van Barneveld and Fredell proved to be the most accurate one. The results of this model agree with the results of the FE model of the test specimen and the in-field specimen. The Wang–Rose model calculates the thermal residual stresses accurately in the case of a test specimen, but the stresses calculated in the case of an in-field specimen are less accurate. No useful experimental data are available in literature from measurements of thermal residual strains on bonded repairs. Therefore experiments were conducted to measure thermal residual strains in bonded repairs. The same repair configurations were used for these experiments. The results obtained with the experiments are compared with FE results. Finally, the temperature distribution calculated by the analytical models is compared with the temperature distribution measured during the experiments of the in-field specimen. The influence on the thermal residual stresses of a different temperature field is discussed here, using the FE results.

The use of X-ray diffraction measurements to determine the effect of bending loads on internal stresses in aluminum inclusions embedded in a unidirectional graphite-fibre/PMR-15 composite

A testing methodology for the determination of residual thermal stresses in the polymer-matrix of unidirectional polymer-matrix composites has been proposed in Ref. [1] [Benedikt B, Kumosa M, Predecki PK, Kumosa L, Castelli MG, Sutter JK. An analysis of residual thermal stresses in a unidirectional graphite/PMR-15 composite based on the X-ray diffraction measurements. Composites Science and Technology (in press)]. The methodology is based X-ray diffraction (XRD) measurements of residual strains in embedded metallic particles. The residual stresses in the polymer matrix can be extracted from the X-ray strains in the particles using the visco-elastic Eshelby method for multiple inclusions. The purpose of this work has been to show that the newly developed experimental/analytical methodology can also be applied to composites subjected to external loads, in this case: spherical aluminum particles embedded in a unidirectional graphite/PMR-15 composite subjected to four-point bending loads. The total stresses and strains in the aluminum particles caused by residual thermal stresses in the composite and the applied stresses generated by four-point bending have been determined by XRD measurements under low bending displacements. Subsequently, the total strains and stresses in the aluminum particles have been numerically predicted by applying elastic and visco-elastic laminate theories and the Eshelby method. It has been shown in this research that not only the residual thermal strains and stresses in the aluminum particles and the matrix can be determined by using the proposed technique but also the effect of external loads on the stresses and strains in the particles can be monitored. This research has provided another verification of the newly proposed methodology presented in Ref. [1].

Development of thermal residual strains in a single sided composite patch

The use of composite patching to reinforce aircraft structure is on the increase as it offers advantages over those of rivet fastened metal patches in application. The objective of this research is to determine the thermal residual strains in graphite/epoxy composites on Al-2024 T3 substrate. To realize this, four specimens were produced, of which one was instrumented by bonding several strain gauges on the patch and Al-substrate. Thermal and thermal residual strains were measured as a function of operating temperatures via those gauges.

Thermal Residual Strain in Metallic Samples Subjected to Heating-cooling Cycles: Crystallite Size and Residual Stress Contribution to the X-Ray Profile Broadening

Metallic samples subjected to heating-cooling cycles present Thermal Residual Strain. X-ray diffraction tests showed that the samples after the cycles change in line-profile width. By increasing the maximum cycle temperature, at first, a profile broadening occurs relative to the width observed before the cycles, then a narrowing, when the temperature overcomes a certain value that is proper of each metal. An accurate analysis of the diffraction line profiles was performed on copper samples in order to distinguish the effect on the line width produced by the crystallite size with respect to that produced by residual stresses. At first, our analysis was restricted to one reflection from a (hkl) plane, so, a single-line method for the analysis of X-ray diffraction line width was adopted. Then, the methods for line profile analysis, in which two orders of reflection are considered, were also applied and the experimental results are presented together with those obtained with one reflection.

Strain monitoring in composite patched structures

Bonded composite patch repair is a developing technology that has been used in the aerospace industry for the purpose of improving the mechanical properties of structure. Graphite/epoxy and boron/epoxy have been the main composite patch materials used in current applications and these composites are bonded to the metallic substrate with epoxy based adhesives. For an effective adhesively bonded reinforcement of a plate, sufficient load must be transferred by the adhesive into the reinforcement to prevent the underlying damage from growing. In this paper, strain monitoring was studied in a single sided patched structure. The thermal residual strains were defined in graphite/epoxy composites on Al-2024 T3 substrate. Five samples were manufactured, and several strain gauges were bonded on the patch Al-substrate. Thermal and thermal residual strains were measured after one- and two-step curing at different temperature and the results were compared with each steps as well as previous work.

Aspects of residual thermal stress/strain in particle reinforced metal matrix composites

The influence of inclusion geometry and thermal residual stresses and strains on the mechanical behaviour of a 20 vol% Al 2 O 3 particulate reinforced 6061-T0 Al alloy metal matrix composite is investigated through finite element analysis . The introduction of residual thermal stresses/strains prior to external loading leads to a decrease of the proportional limit, 0.2% offset yield stress and the apparent stiffness. The residual stresses/strains are shown to have a greater effect on the composite behaviour under compressive loading than tensile loading. The residual stresses/strains have little effect on the cyclic behaviour of the composite. In only the second cycle, the difference between the cyclic curves, with and without a thermal history, was 2 MPa. Use of a cube shaped particle, with sharp corners and edges, in the unit cell model led to much greater initial hardening behaviour than spherical inclusions, and therefore a greater 0.2% offset yield stress due to stress/strain localisation at the particle corners and edges. This results in regions of constrained plasticity and high stress triaxiality in the matrix around the particle, producing improved load transfer in the composite. It is shown that inclusion aspect ratio, in the range of 0.5–2.0, has an impact on the yield stress. A minimum yield stress occurred at an aspect ratio of approximately 0.9 with significant increases on either side of this point. The influence of residual stress/strain had a similar effect throughout the aspect ratio range except tensile loading, following thermal treatment, on unit cells with inclusion aspect ratios greater than 1.5 resulted in the highest yield stresses.

Internal strain evolution during heating of Ti-6Al-4V/SCS-6 composite

The characteristics of the residual stresses and their effects on the properties in continuous SiC fiber reinforced Ti-6Al-4V matrix composites (TMCs) have been extensively studied. However, to date, few experimental studies (e.g. Ti-14Al-21Nb/SCS-6) have characterized the thermal residual strain in TMCs at elevated temperatures. Therefore, the authors investigated the evolution of the thermal residual strain during heating of Ti-6Al-4V/35vol% SiC composite. In this study the authors used in situ high temperature neutron diffraction to measure strains: (1) in the matrix ({alpha} and {beta} phases) and in the fiber, (2) for several lattice reflections in each phase and (3) from both axial and the transverse directions. One distinguishing feature is the wide temperature range (from room temperature up to 1,170K) over which the study was performed. Although the proposed application temperature is typically less than 800K, TMCs are subject to higher temperatures during fabrication and may experience high temperature excursions while in service. Therefore, the authors extended the study to the high temperature regime where the matrix starts to undergo a phase transformation between {alpha}{minus} and {beta}{minus}Ti. Measurements from this regime (800{approximately}1,170K) provide insights on; (1) the inelastic relaxation of the residual strains through matrix yielding and creep, (2) the effectmore » of the phase transformation on the residual strains and (3) the effect of the presence of SiC on the matrix phase evolution.« less

The effect of particle shape on ductility of SiCp reinforced 6061 Al matrix composites

To study the effect of particle shape on thermal residual stress and strain distributions in composites, five two-dimension SiCp/6061Al model composites reinforced with spherical, hexagon, square, triangle and shuttle-shaped particles, respectively were analyzed by finite element method (FEM). The results showed that the particle shape has a great effect on thermal residual stress and strain fields in composites. There are a residual plastic strain concentration in the matrix around a pointed particle corner and a serious residual stress concentration in the pointed particle corner. The two concentrations increase with decreasing pointed corner degree. When an external stress is applied, the plastic strain concentration in the matrix around the pointed particle corner and the serious stress concentration in the pointed particle corner which will fracture on a relative low level of applied stress can decrease ductility of the composite. Two 6061 aluminium alloy matrix composites reinforced with general SiC particles and blunted SiC particles were studied on the basis of the FEM analyses. It was found that most very pointed particle corners are eliminated after SiC particles being blunted. Replacing general SiC particles with blunted ones can reduce residual plastic strain concentrations in the matrix and serious residual stress concentration in the particle. Therefore, blunted SiC particles reinforced composite shows a higher ductility than general one. (C) 1999 Elsevier Science S.A. All rights reserved.

In situ monitoring of the fibre strain distribution in carbon-fibre thermoplastic composites1. Application of a tensile stress field

The distribution of residual thermal strains and the mechanical response of carbon-fibre thermoplastic composites on the application of an external tensile stress have been studied. Confocal laser Raman microscopy has been employed to monitor the Raman wavenumbers of the embedded carbon fibres, within a predefined ‘window’ of observation. The application of a tensile stress field on the P75/ PEEK composite induces an internal fibre stress/strain gradient as a result of progressive fibre fracture and matrix microcracking. The spread of the fibre strain distribution is primarily dependent on the magnitude of the residual thermal stresses and the level of applied stress. In cases where the optical monitoring of discontinuities, such as fibre and matrix breaks, is not possible, a statistical approach is pursued for monitoring the micromechanics of failure in these composites.