Elastic-plastic Stress Analysis Research Articles

Elastic-plastic stress analysis of large axisymmetrically deflected shallow thin shells of revolution

The elastic-plastic stress analysis of a large axisymmetrically deflected shallow thin shell of revolution uses equilibrium, strain-displacement and constitutive relationships. A shell with complex deflection constraints and boundary conditions can be analyzed by experimentally determining the strain history along the axis of revolution, the contour along the generatrix of the shell surface, and the elastic-plastic constitutive relationship. The stress history at the axis of revolution is easily derived from the strain history and takes the place of the boundary conditions in the solution of the equation set. The descriptive relationships reduce to three equations and one inequality in terms of location coordinates, radial and normal displacements, radial and tangential stresses, a functional of the second deviatoric-stress invariant, and constitutive constants.

Studies on Thermal Elastic-Plastic Problems (2 nd Report)

It is well known that during welding or cutting, transient thermal stresses and strains are produced in steel structures and these residual stresses could be one of the causes of cold cracking in cooporation with diffusion of hydrogen and restraint rigidity of the structures. In this paper, a new calculation technique of residual stresses and strains due to welding is described.Thermal elastic-plastic stress analysis for one-dimensional problems has been studied for many years. In the previous paper, the authors reported the formulation of the finite element technique based on displacement method which could be applied to two or three dimensional thermal elastic-plastic stress problems. Recently, more complicated and realistic problems could be solved by using powerful numerical methods such as finite element technique, etc., because of the remarkable progress in computer application.On the contrary, the authors present a new calculation method which combines the idea of dividing the whole region into finite elements such as F. E. M. with the modified initial strain method and stress function introduced by Fujimoto. The above-mentioned stress function corresponds to the concept of the influence function studied by Kawai, and since this influence method is a sort of stress method, it is easily understood that the results calculated by this new method could show fair coincidence with the experimental data.It is comfirmed that thermal elastic-plastic stress analysis based on inherent strain method is rather effective compared with the finite element method of displacement type, when more accurate stress distribution is required, and also that calculation time would be much less when many incremental repetitions are needed.

An elastic-plastic stress analysis of quenching when considering a transformation

A finite element formulation of the elastic-plastic stress analysis during quenching is presented considering a transformation to be described by means of the coefficient of thermal expansion which depends on both the temperature and the cooling rate. The stress-strain incremental relation including the term due to quenching is deduced and using this relation the equilibrium equation is able to be deduced to indicate the effect of the transformation. As an example of the formulated theory, a numerical calculation was carried out for a 0·43 per cent carbon steel circular cylinder of 60 mm dia. during water-quenching. The calculated residual stress agreed well with the experimental values determined by Sachs' boring-out technique.

An elastic-plastic stress analysis for a notched bar in plane strain bending

An elastic-plastic stress analysis, which allows for linear work-hardening, has been carried out for a notched bar using the method of finite elements. Good agreement has been found with available experimental data and confirmation obtained of the idea that the strain at the notch surface is nearly constant over a large fraction of the root. However, some interesting differences exist between the present results and those apparently predicted from slip-line field theory. First, there is the surprising result that the maximum stress does not occur at the elastic-plastic interface. Secondly, in considering the stress intensification (the ratio, R, of the maximum stress to the yield stress), it is shown that slip-line field theory apparently over-estimates R at low loads but slightly under-estimates it near to general yield. The results for the stress intensification are used to re-analyse existing experimental data in order to find the temperature variation of the local fracture stress: this is found to be nearly constant over a range of 250°C.

Progress in three-dimensional elastic-plastic stress analysis for fracture mechanics

This paper summarizes progress in the development of finite element methods for three-dimensional elastic-plastic stress analysis in fracture mechanics. The work is directed toward the study of stress states near flaws such as a part-through crack in a pressure vessel wall, and emphasis is placed on the large scale plastic yielding range The development of a computer program with large computing capabilities is described. Special near crack tip elements and general isoparametric elements are employed in problems with two crack configurations. Preliminary results are given for the elastic analysis of a through crack and for the elastic-plastic analysis of a part-through semi-elliptical crack in a plate.

Stresses Due to a Sharp Notch in a Work-Hardening Elastic-Plastic Material Loaded by Longitudinal Shear

A work-hardening elastic-plastic stress analysis is presented for a sharp notch or, as a limiting case, a crack perturbing a remotely applied uniform stress field. Mathematical complexities are reduced through considering the kinematically simple case of antiplane longitudinal shear deformations and by employing a deformation plasticity theory rather than the more appropriate incremental theory. Consequently, a general solution is available valid for any relation between stress and strain in the work-hardening range, so long as the remotely applied stress does not exceed the initial yield stress. When a power law relates stress to a strain in the work-hardening range, the deformation theory solution is also the correct incremental solution at low applied stress levels causing yielding on a scale small compared to notch depth. For cracks, the near crack tip strain field is shown to depend on loads and geometry only through the elastic stress intensity factor when yielding is on a small scale, and the elastic-plastic boundary and lines of constant strain magnitude are circles. Extensive numerical results are tabulated for a crack, 45 deg V-notch, and 90 deg V-notch in power-law-hardening materials, and exhibited graphically for a crack.

Micro and Macro Crack Formation

The formation of cleavage microcracks with a length of the order of one grain diameter is considered to be the initial step in fracture. It is assumed that the stress concentration required for cleavage is supplied by thick slip or twin bands, and the critical width of these yield bands is calculated. For example, in iron with a grain radius of 10−2 cm, the critical slip band width is 2 × 10−5 cm, and this value is compatible with observations in the vicinity of microcracks. The second stage of crack formation involves the semi-continuous propagation of microcracks to form unstable macroscopic cracks. We postulate that plane strain fractures occur under conditions where thick slip bands are formed in the yielded region in front of an advancing crack. Work required to extend the initial crack is used to calculate the crack extension force, GIc, which is required in linear fracture mechanics. In the case of iron, the microcrack extension force, Y, is calculated to be 5 × 103 dynes/cm, and the minimum value of GIc is calculated to be 2.5 × 106 dynes/cm. This approach emphasizes the three conditions required for fracture: 1) a combination of stress and yield band width sufficient to cause local cleavage; 2) sufficient mechanical energy in the system to propagate the crack; 3) the development of a critical value of the initiation stress in order to continue crack extension. These concepts are used to estimate the plane strain transition and the nominal stress for fracture, i.e. plate fracture stress, σn, is estimated from an elastic-plastic stress analysis to be σc/4, where σc is the yield stress at the tensile transition temperature. The tensile transition is chosen as the point at which the yield and fracture stress are about equal, and the plate transition temperature corresponds to the temperature, TC, at which the yield stress has a value of σc/4. We also estimate that crack arrest in steel plates corresponds to an energy absorption, GC = 22.5 × 103 × t/d, where GC is the crack extension force at the transition between plane strain and plane stress (dynes/cm), t is the plate thickness (cm), and d is the grain radius (cm). A reasonably good correlation for GIc and GC calculated and tested, is obtained. We also use tensile transition data to estimate a plate transition temperature and a critical tensile stress for crack propagation. These are combined with a suggested minimum value of the crack extension force, GC (arrest), to provide the basis for a fracture-safe design criterion.

Initial yielding and fracture in notched sheet molybdenum

The initial yielding and fracture initiation behavior of wrought stress-relieved and recrystallized molybdenum was investigated at room temperature. The effect of notch severity and grain size on the nature of plastic flow in notched sheet tensile specimens was investigated by means of photoelastic coatings. The nature of fracture initiation in notched sheet tensile specimens was studied through the use of pre-polished and etched tandem notch specimens. Application of the Griffith-Orowan theory for crack propagation and the Cottrell criterion for crack initiation reveal that the effective surface energies for crack propagation and crack initiation are of the same order of magnitude, which is 10 3 ergs/cm 2. This finding is supported by the experimental observation that no microcracks were found. Plastic flow regions determined experimentally from the photoelastic coating studies were shown to be in good agreement, both qualitatively and quantitatively, with theoretical results predicted by elastic-plastic stress analyses. Initial yielding at the notch root was found to occur at the same nominal stress level for the given material condition, independent of the magnitude of the stress concentration factor. This nominal stress in the notch section was very nearly equal to the smooth tensile yield stress.