Analysis Of Large Plastic Deformation Of Elasto-plastic Solids

2y ago
87 Views
3 Downloads
297.15 KB
17 Pages
Last View : 20d ago
Last Download : 2m ago
Upload by : Rafael Ruffin
Transcription

Analysis of large plastic deformation ofelasto-plastic solids Friction involves large plastic deformation. There are different ways of solving thedeformation of elasto-plastic solids. Also upper- and lower-bound solutions, whichare approximate solutions, can be very usefulin engineering. One of the methods used is the slip-line fieldmethod, which gives a physical feel for thedeformation process. It is an exact analysis fordeformation of rigid-perfectly plastic solids.

Classification of partial differentialequations Three different types of pd equations:– Elliptic (elastic deformation)– Parabolic (heat transfer, mass transfer)– Hyperbolic equations (wave propagation, plasticdeformation

Classification of partial differentialequations Consider the following second-order partialdifferential equation: 2z 2z 2za 2 b c 2 e x y x yBoundary conditions: z z, andare specified.z, x y

Classification of partial differentialequations z zand may be expressed as x x z 2 z 2zd( ) 2 dx dy x x x yThen the variation of z 2z 2zd( ) dx 2 dy y x y y 2z 2z 2z, and 2 .We have three equations and three unknowns,,2 y x x y

Classification of partial differentialequationsSolving for 2z,2 xN 2z D x 2Depending on whetherD equal to orgreater than 0,the pde represents different physical phenomena.b 2 - 4ac 0, elliptic equation.b 2 - 4ac 0, hyperbolic equation.b 2 - 4ac 0, parabolic equation.

The Upper- and the Lower-Bound Solutions We want to get approximation solutions forlarge deformation of rigid-perfectly plasticsolid in plane strain. We have to satisfy–––––Equilibrium condition (F ma)Geometric compatibilityStress-strain relationship (constitutive relationship)Yield conditionBoundary conditions

The Upper- and the Lower-Bound Solutions Lower bound solutions are obtained if wesatisfy– Equilibrium condition– Yield condition– Boundary conditions on stress Consider the punch indentation problem. Thelower-bound can be obtained as

The Lower-Bound Solutionsx2p0ABx14k2k2k2k4kFigure by MIT OCW.2kRigid

The Upper-Bound SolutionsThe upper-bound-solutions are obtained bysatisfying the following for an assumeddisplacement field:1.2.3.Incompressibility conditionGeometric compatibilityVelocity boundary conditions.

The Upper-Bound Solutionsx2pq displacementof indentationax1BCA(all angles 45o)Figure by MIT OCW.

The Lower- and the Upper-Bound SolutionsThe lower bound solutionp 4kThe upper bound solutionp 6k

The Slip-line Field SolutionsThe stresses can be represented in terms of twoinvariants, p and k, asGraph removed for copyright reasons.See Figure 3.A1 - bottom in [Suh 1986]: Suh, N. P. Tribophysics. EnglewoodCliffs NJ: Prentice-Hall, 1986. ISBN: 0139309837.The Tresca yield condition:σ I σ III 2k

The Slip-line Field Solution for AsperityDeformationDiagram removed for copyright reasons.See Figure 3.A1 - top in [Suh 1986]: Suh, N. P. Tribophysics. EnglewoodCliffs NJ: Prentice-Hall, 1986. ISBN: 0139309837.

The Slip-line Field Solution for AsperityDeformation1.0a q20o15om 0.510o5o0o015q'3045Figure by MIT OCW. After Suh, N. P., and H. C. Sin. "The Genesis of Friction." Wear 69 (1981): 91-114.

Analysis of large plastic deformation of elasto-plastic solids Friction involves large plastic deformation. There are different ways of solving the deformation of elasto-plastic solids. are approximate solutions, can be very useful in engineering. One of the methods used is the slip-line field method, which gives a physical feel .

Related Documents:

plastic deformation during the fracture. A ductile fracture is characterized by considerable amount of plastic deformation prior to and during the crack propagation. On the other hand, brittle fracture is characterized by micro-deformation or no gross deformation during the crack propagation. Plastic deformation that occurs during ductile

plastic deformation and crack propagation. Furthermore FEM elasto- plastic analysis coupled with transient heat condition analysis was performed. The analytical results were good agree with the experimental ones and the propriety of this non-contact measurement system of plastic deformation and fracture process by theromgraphy system was shown. .

deformation and microstructural evolution of polycrystalline ice. Based on the findings of the deformation experiments and microstructural observations, we discuss the effects of microparticles and GBs on the deformation of ice-sheet ice, and we propose a possible reason for the observed rapid deformation of ice-age ice. 2. EXPERIMENTAL .

Fig. 1 Deformation of Shear Wall Subjected to Lateral Load Shear Expansion Flexural Deformation Deformation Fig. 2 Components of Deformation External Force 8 Curvature Rotation Flexural Bending Moment Deformation Fig. 3 Distribution of Rotation of a Cantilever Type Shear Wall (Pull out of Steel at Base is Neglected) B(o,h) 8 ' B c(0,h) toJ-O 0(0,0)

1. Plastic deformation of the surface 2. Crack nucleation at the sub-surface due to plastic deformation 3. Crack propagation from these nucleated cracks due to plastic deformation 4. Creation of loose wear sheets Four mechanisms of delamination wear

deformation, and contact area, are normalized in a logical way that consolidates them as much as possible. This normalization is often relative to a known elastic solution (such as Hertz contact theory) or to the initiation of plastic deformation. The initiation of plastic deformation can sometimes be found analytically by using

Plastic bottles are responsible for 15% of total plastic consumption in Austria.13 According to the new BMK study, 300,000t of plastic - including 49,000t of plastic bottles - were put on the market in 2018. In total, 1.6 billion plastic bottles are placed on the market every year, which equals 181 plastic bottles per Austrian.14

Proposed installation of underground storage tank (USTs) within groundwater protection zones (GPZs) has led to some conflict between the EA and developers in the past. Although standards for