The main difference in implementing a linear viscous or any other kind of rate dependent model compared to a rate independent model arises in the evolution equation for stress and deformation resistance. As we stated before the linear viscous model is a particular instance of the plastic potential function (5-4) with rate sensitivity m=l: Ф […]

By introducing a reference configuration in the deformation equations, any configuration in the deformation process can be expressed in that reference configuration. Figure 5-8 shows the displacement of a particle from its initial position ‘“’x to the current position ‘x. The particle’s reference position can be related to both deformed positions through a motion: x […]

Rate independent plasticity occurs at low temperatures, roughly in the temperature range below 0.57^. The deformation is due to dislocation glide and strain rate due to thermal fluctuations plays no significant role. The relaxation time is zero. In rate independent plasticity the total strain rate is decomposed into elastic and plastic strain rate. Introduce the […]

Thermal-elastic-plastic constitutive models decompose the total strain rate ej01 into the elastic ЄуЄ, plastic due to rate independent plasticity, thermal є* consisting of thermal expansion and creep strain rate ej. During phase transformations additional terms, , i. e., the strain rate volume change associated with the transformation and єіЬр, i. e., the strain rate transformation […]

Accurate modeling of the development of residual stresses and strains in welded steels requires realistic modeling of the microstructural evolution. It is possible to obtain accuracy comparable to experimental measurements. In the equations of continuum mechanics, the parameters such as thermal conductivity, elasticity tensor, the internal variables controlling plasticity or visco-plasticity are sensitive functions of […]

5.1 Introduction and Synopsis The thermal cycle imposed on any welded object causes thermal expansions and contractions to occur that vary with time and location. Since this expansion is not uniform, stresses that appear in hot regions near the weld are restrained by cooler regions further away. Plastic deformation, occurring as a result of these […]

The hardness of the HAZ is a very good indicator of its susceptibility to cracks and other problems. The hardness at any point in the HAZ can be calculated using the rule of mixtures. Once the volume fractions of ferrite, pearlite, bainite, martensite and austenite are known, then the rule of mixtures can be applied […]

Sometimes an estimate of the steady state micro structures is desired in a temperature field computed by a transient time marching analysis. This kind of temperature field is frequently available in published data. To estimate the micro structures is to explore further the values of the old calculations. This test was performed on a mesh […]

The Figures in this section show the state at the rear end of the mesh or flow lines. In the regular mesh next to the filler material, each element has a depth of 2.375 mm in the y — direction. In the upstream area, there is no change from the initial microstructures, since the incoming […]

The microstructures were computed first for the temperature field, Figure 4-10, obtained from ref. [25]. The steady state temperature field was computed on a mesh with about 12,000 elements. The welding speed was 1.5 mm/s. Weld pool size and shape were measured from an experimental weld. The maximum length was 35 mm, the maximum width […]