Elastic-perfectly Plastic Material Model Research Articles

Stochastic fatigue damage accumulation in a T-welded joint accounting for the residual stress fields

The residual stresses that occur as a result of nonhomogeneous heating and cooling during welding may have a significant effect on the accumulation of fatigue damage in a welded joint. The problem is complicated not because of the complex spatial distribution of the residual stress fields, but because those fields typically change under an applied load. The present study considers the effect of residual stresses on fatigue damage accumulation in a welded joint subjected to stochastic loading. The influence of residual stresses on stochastic fatigue damage accumulation is accounted for by a simple approach based on an elastic–perfectly-plastic material model and the Gerber correction factor. The model assumes that the residual stress remaining at the critical location depends on the largest nominal stress ever endured by a welded joint. The model predicts that the residual stresses during stochastic loading randomly decay to zero. The effect of material yielding is additionally investigated by considering an elastic–plastic material model with linear kinematic hardening. The residual stresses in this case are computed through Monte Carlo simulations. It is demonstrated that the effect of material hardening is to reduce the rate of residual stress decay and thus to accelerate the rate of fatigue damage accumulation.

Finite element analysis of subsoiler cutting in non-homogeneous sandy loam soil

A verified finite element model will be a cheap and useful tool in the development procedure of subsoilers and other soil loosening devices, and can be used to investigate and analyse the performance of resulting prototypes. This study was undertaken to emphasis that the finite element method (FEM) is a proper technique to model soil cutting processes in non-homogeneous soils. This method was used to investigate and analyse soil loosening processes. The effect of geometry on subsoiler performance was investigated by the FEM and compared to results of soil bin tests for four subsoiler geometry types; S1 – vertical shank with 31° angle inclined chisel, S2 – vertical shank with 23° angle inclined chisel, S3 – vertical shank with 15° angle inclined chisel and S4 – 75° rake angle shank with 15° angle inclined chisel. The research was done at the Department of Agricultural and Environmental Engineering, PANNON Agricultural University from 1995 to 1997. A three-dimensional FEM model was developed for cutting of non-homogeneous sandy loam soil by a subsoiler having a chisel and shank with different angles and effective cutting widths. The numerical analysis was performed with COSMOS/M 1.71 FEM software (Structural Research and Analysis Corporation, CA). The soil material was considered as elastic-perfectly plastic, and the Drucker–Prager elastic-perfectly plastic material model was adopted with the flow rule of associated plasticity. Soil-tool interaction was simulated adopting Coulomb's law of friction. Total draught force calculated from the FEM model for different subsoiler geometrical types ranged from 12.43 to 15.32 kN. For the S2 subsoiler, that had a vertical shank and an inclined chisel of 23° angle, the chisel and shank contributed to the total draught force by nearly 60 and 40%, respectively. The FEM model consistently over-predicted the measured subsoiler draught force at all chisel angles. The over-prediction of draught estimation ranged from 11 to 16.8% for a non-homogeneous model and from 15 to 18.4% for a homogeneous one. The smallest draught force, measured (11.20 kN) and predicted (12.43 kN), was recorded for the S4 subsoiler having a shank of 75° rake angle and a chisel of 15° angle. The minor principal stress field showed positions of soil tensile failure situated beneath the chisel as well as within the upper soil layers. Zones under distortion (shear failure) were generated directly in front of the shank and along the whole cutting edge of the chisel extending along a hard pan layer. The S4 subsoiler would consume the least amount of energy and perform proper soil loosening. The FEM proved a good tool for modelling of non-homogeneous soils and development and analysis of subsoiler performance and soil loosening processes.

Tillage Tool Design by the Finite Element Method: Part 1. Finite Element Modelling of Soil Plastic Behaviour

The finite element method calculations of draught and vertical forces, soil deformation and normal pressure distribution on subsoiler face were reported for four subsoiler types. A non-linear, three-dimensional, finite element analysis of the soil cutting process by a standard medium-deep subsoiler based upon the Drucker–Prager elastic-perfectly plastic material model was used. The mathematical construction of the Drucker–Prager model was presented. The material non-linearity of soil was dealt with using an incremental technique. Inside each step, the Newton–Raphson iteration method was utilized. The geometrical non-linearity was solved by using the small strain assumption. A comparison of subsoiler forces for calculations made with the small strain assumption and the updated Lagrange formulation of large displacement was reported for subsoiler cutting in a sandy soil. It was shown that the small strain assumption was more convenient for solving the geometrical non-linearity of a soil tilled down to relatively deep horizons.The theoretical results showed that a well coordinated angle combination of the two parts of the subsoiler made a large reduction in the draught and vertical forces of the subsoiler with a shank angle of 75° and a chisel angle of 15°. On the soil surface in front of the shank, the soil was deformed to produce a wedge-shaped soil upheaval. A maximum upward surface movement of 23·7 cm was calculated when soil tilling was performed with this design of subsoiler. For all the geometrical types of subsoiler studied, concentrations of normal pressure at the outer linking edges between the two parts of the subsoiler, as well as on the bottom corners of the chisel, indicated that during manufacturing these parts should be better supported against wear and deformation. The smallest chisel angle of 15° reduced considerably the pressure values at these two parts, whereas changing the shank rake angle from 90 to 75° only assisted in reducing the pressure values at the outer linking edges.