Stress relaxation

About: Stress relaxation is a research topic. Over the lifetime, 12959 publications have been published within this topic receiving 270815 citations.

Creep and Stress Relaxation in Solder Joints of Surface-Mounted Chip Carriers

Abstract: When a surface-mounted ceramic chip carrier is subjected to thermal cycling, complex stresses and strains are generated in the solder joints. Using strain gauges along with some simple assumptions, we can indirectly measure the shear strain and shear force during these cycles. The force, the strain, and the temperature are related by a Simple linear equation with calculable coefficients. At any temperature, the solder simultaneously undergoes creep and stress relaxation in a process We call "stress reduction.'' The rate of stress reduction is controlled by the conventional constitutive relation in which the rate of change of shear strain at a given temperature is proportional to the shear stress raised to a constant power. The constitutive relation is used to develop an equation for stress as a function of time during isothermal stress, reduction. Experiments confirm this equation over the ,range of -28 tO 97°C. The measured time to half-stress depends on the initial stress. For typical values it was measured as 10 min to 1 h at 97°C, one month at 33°c, and (by extrapolation) 30 Years at - 28°C. Almost all methods for interpreting metal fatigue involve the strain amplitude during cycling. In temperature cycling the shear strain amplitude can be expressed as (BS/ H) \triang \alpha T, where S is the in-plane distance from the center of the carrier to the solder joint, H is the height of the solder joint, \triang \alpha is the expansivity difference and AT is the temperature amplitude. The parameter B is a solder Compliance factor. For small temperature amplitudes, B approaches unity at high temperatures and is 0.8 at 100°C, · but it is only 0.08 at 0°C Thus the ratio between the strain amplitude and temperature amplitude depends on the temperature, and this must be factored into any theory Which is used to explain thermal cycle, fatigue in solder joints of surface-mounted leadless chip carriers.

Creep damage modelling for quasi-brittle materials

Abstract: Softening and time-dependence of fracture are two complex and coupled phenomena that have to be taken into account in order to simulate realistic concrete or rock behaviour. Understanding the interaction between these two phenomena is important to design reliable civil engineering structures subjected to high level loading during a long time. The aim of this paper is to develop a simple time-dependent softening model applied to quasi-brittle materials such as rock or concrete. A three-dimensional constitutive visco-damage model describes phenomena like relaxation, creep and rate-dependent loading using a unified framework. The model could be viewed as a generalisation of a time-independent damage model and is based on strong thermodynamical arguments. A general material stability analysis is proposed in case of uniaxial monotonic loading. Phenomena as creep failure under high-sustained load are explained quite simply within stability theory. Creep failure appears as the manifestation of a bifurcation phenomenon. Consequently, this model is able to predict creep failure for various stress level. Conversely, for low-sustained load, the motion asymptotically converges towards an equilibrium configuration, also called equilibrium curve. As for endochronic models, no initial threshold is assumed. Nevertheless, an apparent elastic domain is identified for constant strain rate tests, which reveals the competition between the internal kinetics of damage and the strain rate imposed on the material.

High-resolution strain mapping in heteroepitaxial thin-film features

Abstract: Heteroepitaxial thin-film features that are lattice matched to the underlying substrate undergo elastic relaxation at the free edges of the feature. To characterize the degree of elastic relaxation, we employed synchrotron-based x-ray diffraction techniques to map the change in lattice spacing in the thin film at a submicron resolution. Measurements were conducted on 0.24‐μm thick, heteroepitaxially grown SiGe strips of various widths on Si (001). A comparison of the SiGe diffraction peak positions across the features provides a real-space mapping of the extent of elastic relaxation as a function of linewidth. The resultant in-plane normal film stress measurements were compared to calculated values from several elastic mechanical models to assess their validity in predicting stress distributions within the features.