Total deformation theory for non-proportional loading

• Published in: The International journal of pressure vessels and piping Vol. 75; no. 8; pp. 633 - 642
• Main Authors: Jahed, H., Lambert, S.B., Dubey, R.N.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.1998; Elsevier
• Subjects: Applied sciences; Computation time; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Mechanical engineering. Machine design; Physics; Pipings, valves, fittings; Solid mechanics; Steel design; Structural and continuum mechanics; Tension–torsion loading; Total deformation formulation; Viscoelasticity, plasticity, viscoplasticity; Computation time; Total deformation formulation; Tension–torsion loading; Pipe; Traction; Modeling; Non proportional load; Stress path; Combined load; Elastoplasticity; Piping; A priori estimation; Non linear effect; Torsion; Numerical convergence; Strain hardening
• ISSN: 0308-0161; 1879-3541
• DOI: 10.1016/S0308-0161(98)00068-4

This study presents a technique to apply a total deformation theory to non-proportional loading cases. A total deformation theory capable of analyzing a sequence of linear non-proportional load steps is proposed. Each linear loading path is defined with reference to its previous loading path, analogous to proportional loading. The application of the proposed formulation to tension–torsion loading of thin tubes and pressure–torsion loading of thick-walled cylinders is carried out. It is shown that for situations where stresses are known a priori, the proposed method gives the same plastic strain field as does incremental plasticity. For situations where stresses are not known a priori, a method to estimate the plastic strain for linear hardening materials is proposed. This method estimates the necessary stress fields using conventional deformation plasticity. These stresses are then used in the proposed total deformation formulation to predict plastic strains. The plastic strain field resulting from this method is compared with finite element results obtained using incremental plasticity. The results are in very good agreement and the proposed method significantly reduces computation time.