Nonlinear Thermal Stress Research Articles

Nonlinear thermal-distortion predictions of a silicon monochromator using the finite element method

Silicon crystal monochromators at cryogenic temperatures have been used with great success at third-generation synchrotron radiation sources. At the Advanced Photon Source the unique characteristics of silicon at liquid nitrogen temperatures (80 K) have been leveraged to significantly reduce the thermally induced distortions on beamline monochromators. Finite element simulations of the nonlinear (temperature-dependent material properties) thermal stress problem were performed and compared with the experimental measurements. Several critical finite element modeling considerations are discussed for their role in accurately predicting the highly coupled thermal and structural response of the optical component's surface distortion to the high thermal heat flux. Once an understanding of the effects of (i) local element mesh size, (ii) area/surface heat flux versus volumetric heat generation, and (iii) uniform volumetric absorbed power versus a depth-dependent absorbed power, a final series of simulations was performed. Depending on the estimated convection heat-transfer coefficient, the final refined finite element model's predictions correlated well with the experimental measurements. In general, the use of the finite element method in predicting the overall thermal and structural behavior of the surface of the optical components with a high heat flux was shown to be quite effective.

A fully non-linear theory of electro-magneto-hydrodynamics

A number of analytical models exist for both electrohydrodynamics (EHD) and magnetohydrodynamics (MHD). At present there are no practical yet consistent models for the combined electro-magneto-hydrodynamic (EMHD) effects which occur quite often in actual situations. This work represents an attempt to develop such a fully consistent analytical model for multi-dimensional, steady and unsteady, compressible and incompressible flows of electrically conducting fluids under the simultaneous or separate influence of externally applied and internally generated electric and magnetic fields. The approach is based on the fundamental laws of continuum mechanics and thermodynamics with all assumptions clearly stated and consistently applied. The resulting second order EMHD model allows for non-linear electric and thermal conduction and electromagnetic stress within the medium. The new model is therefore superior to the existing EMHD models and represents a tractable set of equations suitable for detailed numerical discretization and integration.

Strength of Adhesively-Bonded Thbular Single Lap Carbon/Epoxy Composite-Steel Joints

The static tensile load bearing capability of adhesively-bonded tubular single lap joints if calculated using the linear mechanical adhesive properties is usually less than the experimentally determined one because the majority of the load transfer of adhesively-bonded joints is accomplished by the nonlinear behavior of the rubber-toughened epoxy adhesive. In this paper, both nonlinear mechanical properties and fabrication residual thermal stresses of adhesive were included in the stress calculation of adhesively-bonded tubular single lap carbon/epoxy composite-steel joints. During calculation, nonlinear tensile properties of adhesive were approximated by an exponential equation that was represented by the initial tensile modulus and ultimate tensile strength of adhesive obtained from tensile tests. From the tensile tests and the stress analyses of adhesively-bonded tubular single lap carbon/epoxy composite-steel joints with respect to stacking angles of carbon/epoxy composite adherends, the failure model for the adhesively-bonded tubular single lap carbon/epoxy composite-steel joint under the axial tensile load was proposed with considering fabrication residual thermal stresses.

Influence of Fabrication Residual Thermal Stresses on Rubber-toughened Adhesive Tubular Single Lap Steel-Steel Joints under Tensile Load

The tensile load bearing capability of adhesively-bonded tubular single lap joints which is calculated under the assumption of linear mechanical adhesive properties is usually much less than the experimentally-determined because the majority of the load transfer of adhesively-bonded joints is accomplished by the nonlinear behavior of rubber-toughened epoxy adhesives. Also, as the adhesive thickness increases, the calculated tensile load bearing capability with the linear mechanical adhesive properties increases, while, on the contrary, the experimentally-determined tensile load bearing capability decreases. In this paper, the stress analysis of adhesively-bonded tubular single lap steel-steel joints under tensile load was performed taking into account the nonlinear mechanical properties and fabrication residual thermal stresses of the adhesive. The nonlinear tensile properties of the adhesive were approximated by an exponential equation which was represented by the initial tensile modulus and ultimate tensile strength of the adhesive. Using the results of stress analysis, the failure criterion for the adhesively-bonded tubular single lap steel-steel joints under tensile load was developed, which can be used to predict the load-bearing capability of the joint. From the failure criterion, it was found that the fracture of the adhesively-bonded joint was much influenced by the fabrication residual thermal stresses.

Heat transfer and nonlinear thermal stress analysis of a convective surface mount package

Most prior heat transfer and thermal stress analyses of convective surface mount packages have relied on either an isothermal (constant temperature) model or a constant heat transfer coefficient model. This usually leads to a concern for the accurate estimation of the local temperature distributions and the induced stresses. To release this concern, this paper presents the use of the finite element analysis method in predicting the local temperature and stress distributions of a ceramic ball grid array (CBGA) package. The analysis has included a local heat transfer coefficient model with the thermal boundary condition that was obtained from a previous computational fluid dynamics (CFD) solution. The results are compared with that predicted by the isothermal model and the constant heat transfer coefficient model. Instances where the temperature dependent and elastic-plastic material behavior are significant to produce nonlinear stress response in some components of the modeled package are also examined.

Predictive thermal and mechanical modeling of a developmental MCM

Under development at the Microelectronics Center of North Carolina is a high-performance multichip module (MCM) that utilizes 95Pb-5Sn and indium solders. In this article, a rigorous thermal/mechanical analysis is applied to the module, with specific emphasis on the solder joint reliability. The methodology includes mechanical characterization of solder joints, thermal modeling, linear structural modeling, nonlinear thermal stress simulations, and fatigue-life prediction as a function of chip power dissipation. The results of the analysis provide insight toward design optimization and fatigue life acceleration factors that relate laboratory tests to field use conditions.

Nonlinear thermal and mechanical analysis of step-tapered laminated plate under uniform in-plane load

A method has been developed for the thermal analysis of materially nonlinear carbon fibre reinforced plastic (CFRP) step-tapered laminated plates using a quasi-three-dimensional iso-parametric finite element. The variation with temperature of the coefficient of expansion of CFRP in the transverse direction is included. The nonlinear initial thermal stresses resulting from cooling from the stress-free temperature of 132·2°C (270°F) to 20°C in [+θ/−θ/resin/90°/90°] s and [+θ/−θ/resin/+45°/−45°] s stepped plates were found. All stepped plates were then subjected to a uniform applied stress until first-ply failure was detected inside the laminate according to the maximum strain failure criterion. This nonlinear analysis was based on an initial stress iteration method formulated in a previous paper. In all cases, the resin-rich layer between the laminae that form the step was included. It was found that the initial thermal stresses of some stepped plates are of the same sign as their corresponding cases under an applied tensile stress but without initial thermal stresses included. With initial thermal stresses included, these stepped plates failed at an applied stress lower than for the cases without the initial thermal stresses. In contrast, the initial thermal stress components of other stepped plates are of opposite sign to their corresponding cases under an applied tensile stress only. With the inclusion of the initial thermal stresses, these stepped plates failed at a higher tensile stress than the cases without initial thermal effects. The [+θ/−θ/resin/+45°/−45°] s stepped plates exhibited lower strengths than the [+θ/−θ/resin/90°/90°] s stepped plates. The results suggest that the [+45°/−45°/resin/90°/90°] s laminate is probably better suited to resist tensile loading.

Transient Thermal Stress Analysis of a Plated Through Hole Subjected to Wave Soldering

During a typical wave soldering operation a plated through hole (PTH) is exposed to temperatures which are higher than any rated operating temperatures. Understanding the heat transfer and the potential PTH damage mechanisms, which arise during the wave soldering process, is critical to PTH quality control and reliability. In particular, cracks may be initiated during the wave soldering transient and become manifest only after operational cycling. This paper presents a transient nonlinear thermal stress analysis of a nonsolder filled PTH that is subjected to a typical wave soldering process. A full three-dimensional orthotropic analysis and an axisymmetric analysis with cylindrically anisotropic properties are used and the results compared. Temperature and stress/strain history curves are examined to determine the impact of the wave soldering operation on the PTH fatigue life. The effect of PWB innerplanes on the PTH maximum stress and strain is also investigated.

Nonlinear thermal and mechanical analysis of edge effects in angle-ply laminates

A method has been developed for the thermal analysis of materially nonlinear Carbon Fibre Reinforced Plastic (CFRP) laminated plates using a quasi-three-dimensional iso-parametric finite element. The variation of the linear expansitivity of CFRP lamina with temperature in the transverse direction is included. The nonlinear initial thermal stresses resulting from thermal cooling from the stress-free temperature of 132.22 to 20°C in the [ 0 90 ] s and [±45] s laminates were found. These two types of laminates were then subject to a uniform applied strain ϵ x until failure was detected inside the laminate according to a maximum strain failure criterion. This nonlinear analysis was based on an initial stress iteration method formulated in a previous paper. The [±45] s laminate analysis was carried out with and without resin layers between the laminae modelled. All results obtained were compared with those of previous investigators. It was found that with initial thermal stresses included the [ 0 90 ] s laminate failed at an earlier stage than without initial thermal stresses included. The [±45], laminate with initial thermal stresses included failed at a later stage than that without initial thermal effects and the inclusion of resin layers delayed the failure even further.

Nonlinear thermal stress analysis of a massive concrete structure

This paper describes an effective method for forecasting thermal cracking in massive concrete and compares numerical calculations using the ADINAT and ADINA finite element programs to experimental results obtained on an actual structure.

Non-linear elastic thermal stress analysis with phase changes

The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading.

The Determination of Stresses and Temperatures in Cooling Bodies by Finite Elements

This paper presents a finite element method for solving non-linear heat conduction and thermal stress problems. The nonlinearity is caused by the variation of thermo-physical and mechanical properties of the material with respect to temperature. The distribution of temperature and stress in a cooling body can be followed from the onset of solidification. The method is capable of handling complex geometries and initial non-linear boundary conditions.

Linear and nonlinear thermal gradients — an interpretation of the nuclear Components Code — section III

The nuclear Components Code ∗ ∗ Section III-1971 of the ASME Boiler and Pressure Vessel Code. requires a detailed stress analysis, including the stresses caused by the transient temperature gradient across the thickness of the pressure boundary. By Code dèfinition, this thermal stress is composed of a linear portion (causing secondary stresses) and a nonlinear portion (causing peak skin stress). Using the across-the-thickness thermal transient as a basis of definition, this article derives the general expression for the linear and nonlinear portions of the transient. This derivation may be directly incorporated for evaluation of linear and nonlinear thermal stresses by a minor modification to a standard transient analysis computer code.