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Plane plastic deformation of the shear deformation lines

os ~ (plane stress) (10) can be obtained from the above equation the following conclusions: a, 2> 0, plane shear at any point there are two lines,[link widoczny dla zalogowanych], the composition of curvilinear non-orthogonal in general, only when a 9O ', the curve network is orthogonal. At this point the basic equations of plane stress is a hyperbolic-type {b, 2 10,[link widoczny dla zalogowanych], the time degenerate into a family of cut nets do not intersect the curve, then the basic equations of plane stress is parabolic} c, no real solution, which does not exist in plane shear line, the basic equation is elliptic. Three cases above can be Figure 3: thick solid line is the 2> 0 and the {thin solid line is the case of cutting line does not exist; the transition point is 2 10 situation. In order to facilitate understanding of the results of this paper, some of the plastic plane problems are given special side; i, plane strain deformation: one (11) mouth of a 45. b, tensile deformation: a mouth of a 5444c, uniaxial compression deformation: 2 a a = 35. 16d, such as two-way and two-way pull such pressure deformation: Shan = 0 does not exist. Above four cases can be found in Figure 3 the corresponding point is shown in Figure 4, several special deformation of the shear deformation of line. L Chong-way one-way pull distressed compression stress state (3 swear allegiance to the stretching around 4 cents like the typical shear stress-like blog shear line 4 the relationship between line and Mohr circle 84 - Fang Yi: plastic deformation of the shear plane shear deformation lines,[link widoczny dla zalogowanych], said two-dimensional Mohr circle is a powerful tool for stress, therefore, shear deformation stress state line at any point can be expressed by Mohr circle. Figure 5 represents the state of the four stress Mohr circle: a, plane strain} b, plane stress hyperbolic} c, parabolic plane stress Id,[link widoczny dla zalogowanych], elliptic plane stress. Since the issues discussed is the two-dimensional,[link widoczny dla zalogowanych], so is limited to describe the stress state in a three round, we use coarse solid line. shear stress state line, corresponding to a = line with the thick solid line circle intersection. According to Mohr circle intersects the line with the situation, there may be three cases: i) d has been rounded lines and thick solid lines are two intersections, then the two intersection points to correspond to the shear line of two intersecting {ii) d = a straight line and thick solid line circle only one cut point, then the point corresponds to a shear line; iii) d straight line and thick solid line circle no intersection, then there is no cut line. According to Mohr four point shear stress state line can be expressed as: a r = fu \5 Typical stress state the stress Mohr circle (1) plane strain (2) dl <0 for plane stress state (3) aI 0 plane drought stress (I); 0 of the plane stress state of a Chi 4 Conclusion No. 85 of Qingdao University l2 Volume 4.1 of the proposed cutting line theory, the two-dimensional plane stress plastic deformation and plane strain problems of the physical characteristics of unity, making the cut line can not only describe the plane strain problem, you can also describe the plane stress problem, and to maximum shear stress slip-line traces defined in the plane stress problem, we can not express the characteristics of deformation. 4.2 Shear deformation at any point line is: the normal deformation along the cutting line is zero, the plastic deformation is shear deformation increases the shear line extension or compression deformation. If there is no elongation along the shear line or compression deformation is plane strain problem} If the shear deformation of the shear line is zero, can be seen from the Mohr circle, this time a principal stress is equal to the average stress through, so the deformation is pure shear line extension of the pure deformation. This issue only when the plane stress equations of parabolic characteristic only exist. 4.3 The concept of shear deformation line can has extended to three-dimensional plastic deformation to be studied further. However, one thing is certain, in the three-dimensional plastic deformation, but also the existence of such position. that the existence of three-dimensional deformation of a body section, the section of the normal stress equal to the average stress, which is the section of law to the strain rate is zero. For example, any cross-section of the normal stress with principal stress can be expressed as = 1 + identified. + n {If so es. one, then l + m. + n . = 01 where, mouth, mouth is a partial amount of principal stress, 1 = m-n a _ on the type of a solution. 34.4 Mohr circle represents the shear deformation with the line, the application of the Mohr circle proposed a new way This shows that the information contained in Mohr circle remains to be studied further. 1L.M. Katja Ivanov reference book. ZHOU Cheng commission translation. plasticity theory (Second Edition). People Education Press. 198Z in June 2R.A.C. Adams brother special book. Lord Master Zhong Ren such as translation. Ha of plastic theory in its application in metal forming. Machinery Industry published on April Rui Du .1983 _ a

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