Inelastic Strain Field Research Articles

Software application for evaluating interfacial stresses in inelastic symmetrical laminates with free edges

Authors propose herein a software application called DEILAM, which is able to evaluate the free edge effects in multilayered inelastic structures that essentially bear tensile loads. The inelastic behavior of both layers and interfaces are take into account. The program therefore involves inelastic strain fields in the layers and fields of displacement discontinuities at the interfaces. These inelastic fields, such as thermal strains or interface sliding, are assumed to be known by the user. For evaluating the 3D interfacial stresses, the program uses an approximate model that models the laminate by a superposition of Reissner plates coupled by interfacial stresses. Calculations show that no singularities exist for the model even at the edge and results converge quickly. Calculations are validated by comparing the results with finite element calculations and with Pagano’s local model. Analysing the maximum values of the interfacial stresses for some examples, the authors then show how the software can help predict the place where delamination might appear. Since delamination is a critical failure mode that often takes place at free edges, this program with a delamination criterion involving the maximum interfacial stresses can prove to be an important tool in composite structure design.

Higher-order theory for periodic multiphase materials with inelastic phases

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress and inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model and with finite-element results for transverse loading.

Integrated Micro/Macro Approach for Laminate Composite Analysis: Applications to Turbine Blades

An integrated micro/macro mechanical procedure for structural analysis of unidirectional metal matrix composites is proposed. The micromechanical analysis is performed with the composite cylinder assemblage model or the representative volume element approach. The macroscopic stress-strain relation is based on a modification of the vanishing fiber diameter theory and the concept of a smeared finite element. The fibers are considered to be linear elastic, and the matrix viscoplastic behavior is described by the Bodner and Partom model (Bodner, S. R., Review of Unified Elastic-Viscoplastic Theory, Unified Constitutive Equations for Plastic Deformation and Creep of Engineering Alloys, edited by A. Miller, Elsevier Science, New York, 1987, pp. 77-106). The overall composite behavior is assumed to be elastic-viscoplastic. Two types of material systems are used: SCS-6/Ti-15-3 and SCS-6/Tiβ21-S. Both sets of material systems exhibit isotropic and/or kinematic hardening under specific conditions of temperature and loading. The proposed methodology is validated with experimental and analytical results available in the literature. After the validation process, this methodology is applied to a three-dimensional finite element model of a [0/90] 2s SCS-6/Tiβ21-S turbine blade tip. Aerodynamic and centrifugal loading are considered to be acting at the same time. The turbine blade tip inelastic strain field is presented.

Thermomechanical behavior of micron scale solder joints under dynamic loads

Recent trends in reliability and fatigue life analysis of electronic devices have involved developing structural integrity models for predicting the operating lifetime under vibratory and thermal environmental exposure. Solder joint reliability is the most critical issue for the structural integrity of surface mounted electronics. Extensive research has been done on thermal behavior of solder joints, however, dynamic loading effects to solder joint fatigue life have not been thoroughly investigated. The physics of solder joint failure under vibration is still not very clear. This paper presents a test program which was performed to study inelastic behavior of solder joints of BGA packages. A concurrent loading unit is used which consists of a thermal environmental chamber and an electrodynamic shaker. Laser Moiré Interferometry was used to measure the whole deformation field of the prepared specimen surface. The corresponding inelastic strain field is then calculated. It is found that at elevated temperature, vibration and shock can cause the accumulation of inelastic strains and damage in solder joints. In this paper, contrary to the popular belief that all vibration-induced strains are elastic, it is shown that vibration can cause significant inelastic strains.

Analytical evaluation of singular integral in boundary element analysis of inelastic strain problem.

An analytical evaluation method of a singular domain integral in BEM inelastic analysis is described in this paper. A high order singular domain integral term originated from an inelastic strain rate is present in the internal stress rate formulation and, therefore, it is very difficult to calculate its principal value by numerical integration. However, an accurate evaluation of the internal stress rate is important to obtain a correct inelastic strain field at each load increment stage of nonlinear material BEM analysis. In the present paper, we derived a fully analytical form of the singular integral term for a plane problem by applying a triangular polar coordinate transformation which can reduce the order of singularity by one degree. Internal stresses for thermal strain problems and a plastic strain problem are calculated by this method. The accuracy and effectiveness of this method is discussed, compared with the conventional numerical integral method.

Inelastic structural analysis of the mars tandem mirror reactor

The effects of radiation on the structural performance of fusion reactor structures is recognized as a major issue for the development of fusion reactor technology. Neutron irradiation changes the mechanical properties of structural components resulting in a general degradation of these properties. In addition to the mechanical loads (pressure and weight) and the thermal strains, non-uniform inelastic strain fields are induced by radiation swelling and creep in fusion structures. In this paper, we describe a new computer code, STAIRE, for ST ress A nalysis I ncluding R adiation E ffects. This code is based on standard beam theory for pipe-bends. The theory is modified in two areas: (1) consideration of the pipes' cross-section deformation as the radius of curvature changes; and (2) inclusion of inelastic radiation and thermal strains (swelling and creep). An efficient analytical/numerical approach is developed for the solution of indeterminate beam problems. As an application of the method, the stress distribution and deflections of toroidal blanket pipes in the Mirror Advanced Reactor Study (MARS) are evaluated. Swelling strains are identified as a major source of stress and deformation in the proposed blanket design, and possible solutions to the problem are outlined.

Initial Strain Field and Fatigue Crack Initiation Mechanics

On single aluminum crystals under cyclic loadings, fresh slip lines appeared during the reversed loading, lying very close to, but not coincident with the slip lines formed in the forward loading. These slip lines indicate the start of extrusion or intrusion as commonly observed in fatigue specimens. An initial stress field is present in all metals. The initial stress field favorable to the aforementioned sequence of slip is one having a positive shear stress in one thin slice P and a negative one in a closely located thin slice Q. A forward loading causes a positive shear stress, which is of the same sign as the initial shear stress in P, but of opposite sign to that in Q. Hence the shear stress in P will reach the critical value first to cause slip. Due to the continuity of the stress field, slip in P relieves not only the positive shear stress in P but also in Q. This has the same effect as increasing negative shear stress in Q. During the reversed loading, Q has the highest negative shear stress and hence slides. Similarly, this slip causes P to be more ready to slide in the next forward loading. This process is repeated to cause a monotonic alternate sliding in P and Q. In this way, an extrusion or intrusion is nucleated. A crack can be started from an intrusion. The thin slices P and Q are considered to be in a most favorably oriented crystal located at a free surface. An initial stress field giving positive shear stress in P and negative in Q is calculated from an assumed initial inelastic strain field which, in turn, can be caused by distribution of dislocations. The buildup of plastic shear strain in P and Q causing the start of extrusion or intrusion is shown.