Instytut Podstawowych Problemów Techniki

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When analysing the problem of the positioning accuracy of robot manipulators it is important to know how far random deviations of the hand may be from the desired position if the joint positioning errors possess a normal distribution. Two methods of determining the ellipses and ellipsoids of probability concentration are compared. The first of them is based on the standard procedure of the probability calculus. The second approximate method consists in finding at first the polygon or polyhedron of the positioning accuracy, and then in finding the ellipse or ellipsoid with principal axes and second order moments coinciding with those of the polygon or polyhedron, respectively. Examples of application demonstrate that these two methods give very close results.

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Slip-line solutions are presented in an attempt to analyse the role of internal strain concentrations in the mechanics of ductile fracture. Interaction between variously oriented cracks leading to local microfractures is examined. Examples of simple experimental modelling substantiate theoretical analysis.

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The technique of statically admissible plastic stress fields is used in the plastic design of complex connections -of steel structures. An appropriate stress field gives a safe estimate of the shape of the connection design. Complex three-dimensional stress fields are composed of elementary subfields. Thus the procedure of plastic design consists in appropriate arrangement of subfields into a complex system of stresses.

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The technique of statically admissible plastic discontinuous stress fields is used in the plastic design of machine parts of complex shape. If the shape of the part is given the stress field is used to find a lower bound on the bearing capacity. In the case of plastic design an appropriate stress field gives a safe estimate of the shape of the designed part. Complex three-dimensional stress fields are composed of elementary sub-fields, all geometrical and statical parameters of which are tabulated in order to simplify the design procedure. Thus the procedure consists in appropriate arrangement of sub-fields into a complex system of stresses.

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Experimental results for thirtysix thin walled tubular specimens of M-63 brass are presented in a study of the effect of biaxial cyclic loading in the first and second quadrant of the principal stress plane on the shape of the yield surfaces. These results show that tested material strained cyclically beyond the initial yield locus works under a fully elastic regime after a few cycles of the initial transitory period.

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The complete solutions for the plastic bending of deeply notched bars are presented for certain configurations of the notch. Extensions of the stress fields into the rigid regions have been obtained by superimposing two fields of the type given by J.F.W. Bishop for axially loaded notched bars, or one such a field, on an uniaxially tensioned (or compressed) strip. For other shapes of the notch the method breaks down; it then gives lower bounds on the yield moment.

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Upper bounds on the yield point load factor for notched bars with finite thickness and small shoulder ratio c/h, are presented and later compared with experimental results. Five sets of specimens of aluminium alloys were tested. It was found that the yield point load generally coincides with the theoretical upper bound, although the influence of the notch geometry and ductility of the material can be observed.

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Experimental results for fifty-six specimens of an aluminium alloy are presented in a study of the effect of the prestraining path on the shape of the yield surfaces. A special experimental technique has been applied, consisting of cutting out flat specimens from the prestrained sheet material. Experimental results show that if two various loading paths have different initial sectors and a common final sector, the influence of these initial sectors on the yield surface is the smaller the longer is the final common sector. A theoretical analysis of that problem on the basis of the kinematic workhardening rule is also presented.

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The plastic incipient flow of V-notched axially symmetric bars with different slope of the two generators is considered using theTresca yield criterion and associated flow rule. The experimental results show good agreement with theoretical solutions.

Słowa kluczowe:

Yield Criterion, Flow Rule

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Theoretical and experimental results are presented for plastic flow of axially symmetric notched bars. The slip-line fields have been calculated numerically using the Shield theory of axially symmetric plastic flow. The load factors obtained from the theoretical solutions differ only slightly from those for plane strain conditions. Two sets of specimens were investigated in order to obtain the actual load factors for V-shaped and rounded notches. The agreement between the theory and experimental results is satisfactory. In the last series of experiments the influence of the diameter of the bar outside the notch was investigated and later compared with the theoretically estimated value of that diameter.

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Experimental results for twenty-eight tubular specimens of a M-63 brass, subjected to combined biaxial tension, are presented in the study of the effect of prestraining on the shape of the yield surface. Yield surfaces are found for various definitions of the yield locus. The strain increments are also shown in the stress plane in order to compare their orientation with the normality criterion. Moreover, the lengths of elastic and plastic strain increment vectors are compared at different moments of loading.

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Streszczenie:

Experimental results for twenty-eight tubular specimens of a M63 brass, subjected to combined biaxial tension are presented in the study of the effect of prestraining on the shape of the yield surface. Yield surfaces are found for various definitions of the yield locus. The strain increments are also shown in the stress plane in order to compare their orientation with the normality criterion. Moreover, the lengths of elastic and plastic strain increment vectors are compared at different moments of loading.

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