Correction Formulae for the Stress Distribution in Round Tensile Specimens at Neck Presence [electronic resource] /
Gromada, Magdalena.author.
Mishuris, Gennady.author.
Öchsner, Andreas.author.
The monograph deals with methods to determine mechanical properties and evaluate the flow curve of ductile materials from the tensile test. It presents classical hypotheses concerning the onset of neck creation as well as the state of the art in determining the mechanical properties from the tensile test, with emphasis on the consequences of the neck formation. It revises derivations of formulae for the stress distribution in the minimal cross-section of the axisymmetrical specimen in the classical approaches proposed by Bridgman, Davidenkov / Spiridonova and Siebel as well as in the less famous formulae derived by Szczepinski and Malinin / Petrosjan. The revision is completed with solutions evaluated by the authors. In the monograph, the simplifying assumptions utilised in the classical approaches were carefully verified by numerical simulations accompanied by theoretical analysis. Errors imposed in the evaluation of the average axial stress acting on the minimal cross-section as a result of every particular simplification are estimated. The accuracy of all formulae to evaluate the flow curve is discussed. The significance of a high accurate determination can be seen in the context of numerical simulation (e.g. finite element computations), where the total error and accuracy is partly based on the accuracy of the material input.
Description based upon print version of record.
Correction Formulae for the Stress Distribution in Round Tensile Specimens at Neck Presence; Preface; Contents; Notation; 1 Characterisation of the Tensile Test; Abstract; 1.1...Introduction; 1.2...Determination of the Flow Curve; 1.3...Phenomenon of the Neck Creation; 1.4...Analysis of the State of Knowledge Regarding the Mechanical Properties Determination from the Tensile Test at the Neck Presence; References; 2 Stress Distribution in the Sample Neck during the Tensile Testing; Abstract; 2.1...Problem Description based on Deformation Theory of Plasticity
2.1.1 Consideration of the Axial Symmetryaxial symmetry2.1.2 Equilibrium Equationsequilibrium equations; 2.1.3 Yield Conditionsyield conditions; 2.1.4 Basic Relationships; 2.2...Problem Description based on Plastic Flow Theory; 2.3...Formulae Derivation based on Bridgman Approach; 2.3.1 Derivation of the Basic Relationships in Deformation Theorytheory of plasticity:deformation theory of plasticity; 2.3.1.0 The First Simplifying Assumption; 2.3.1.0 The Second Simplifying Assumption; 2.3.1.0 The Third Simplifying Assumption; 2.3.1.0 The Fourth Simplifying Assumption
2.3.2 Derivation of the Basic Relations in Plastic Flow Theorytheory of plasticity:plastic flow theory2.3.2.0 The First Simplifying Assumption; 2.4...Formulae Derivation in Davidenkov and Spiridonova Approach; 2.5...Formulae Derivation in Siebel Approach; 2.6...Formulae Derivation in Szczepinacuteski Approach; 2.7...Formulae Derivation in Malinin and Petrosjan Approach; 2.8...New Formula Derivation by Generalisation of the Relation for the Curvature Radius of Longitudinal Stress Trajectory from the Classical Approaches; 2.9...New Formula Derivation on the Base of Other Set of Assumptions; References
3 Formulae Verification for the Flow Curve Determination Due to Numerical SimulationAbstract; 3.1...Description of the Numerical Simulation; 3.2...Verification of Simplifying Assumptions Applied in Classical Approaches; 3.2.1 Verification of Simplifications by Means of the Numerical Simulation; 3.2.2 Verification of Simplifications Due to Analytical Analysisanalytical analysis; 3.2.2.1 Assumption of the Equality of the Radial and Circumferential Stresses; 3.2.2.2 Assumption of the Constancy of the Yield Stress in the Minimal Section Plane
3.2.2.3 Assumption of the Formula Form for the Curvature Radius of the Longitudinal Stress Trajectory3.3...Verification of the Formula for Determination of the Strain Intensity; 3.4...Formulae Verification for the Average Normalised Axial Stress in the Minimal Section Plane; References; Summary; Index
Includes bibliographical references and index.
The monograph deals with methods to determine mechanical properties and evaluate the flow curve of ductile materials from the tensile test. It presents classical hypotheses concerning the onset of neck creation as well as the state of the art in determining the mechanical properties from the tensile test, with emphasis on the consequences of the neck formation. It revises derivations of formulae for the stress distribution in the minimal cross-section of the axisymmetrical specimen in the classical approaches proposed by Bridgman, Davidenkov / Spiridonova and Siebel as well as in the less famous formulae derived by Szczepinski and Malinin / Petrosjan. The revision is completed with solutions evaluated by the authors. In the monograph, the simplifying assumptions utilised in the classical approaches were carefully verified by numerical simulations accompanied by theoretical analysis. Errors imposed in the evaluation of the average axial stress acting on the minimal cross-section as a result of every particular simplification are estimated. The accuracy of all formulae to evaluate the flow curve is discussed. The significance of a high accurate determination can be seen in the context of numerical simulation (e.g. finite element computations), where the total error and accuracy is partly based on the accuracy of the material input.
Mechanics.
Mechanics, Applied.
Computer mathematics.
Materials science.
Solid Mechanics.
Computational Science and Engineering.
Characterization and Evaluation of Materials.