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Investigation and Development of mechanics designing in composite material and evaluation of crack problem mechanism

Abstract

In continuing done works that in a product design process, many complex multi objective optimization problems occur. Mechanical Engineers need to improve the design using simulation and optimization techniques. There are many challenging issues in solving complex engineering designing problems. The first issue is how to improve the design efficiency. Current industries need to develop high quality products in a short time due to competition or design cycle requirements.

Cracking in the system is responsible for the reduction of strength for the vast majority of engineering materials. The object of this research is to introduce the Linear Elastic Mechanics to evaluation of designing knowledge on the cracking behavior of Composite Materials. This has implications for the science of the subject-basic understanding and modeling-and for practical considerations to aid high performance engine development. Several models will focus in this study. Most engineering composite designers exhibit failure behaviors that are governed by anisotropic and heterogeneous characteristics. In this thesis will use spatial rescaling to reduce plane elasticity problems for designing materials.

Guided by this technique and other analytic results, a systematic analysis is conducted for specimens to investigate and evaluation the role of material orthotropy in fracture behavior of unidirectional composites. All numerical calibrations are presented with fitting formulae in the relevant parameter

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regimes. The effect of material orthotropy on fracture behavior of unidirectional composites is thus quantified.

1. Introduction

Some basic limitations do exist due to practical systems and fabrication considerations, such as, physical compatibility (e.g. coefficient of thermal expansion), chemical compatibility (e.g. inherent stability of compound pairs), interfacial properties and interactive effects etc. Due to these features, micro defects could be introduced during process. It is generally accepted that micro defects are responsible for the reduction of strength for the vast majority of engineering materials. Upon application of loads, damage accumulates because of the presence of micro defects and the applied load. The newly formed damage depends on the interplay of the micro defects, materials, environment, etc. For a majority of materials the interaction results in a macroscopic crack which propagates in a quasi-static fashion until dynamic fracture. Therefore, understanding of fracture phenomena is commonly sought by addressing three basic issues: crack initiation, quasi-static crack propagation and dynamic fracture.

2. Research Motivation

In attempting to control and designing a composite material's properties through the modification of the inter phase and process cycle, there exists many issues which need to be addressed. The chemical and thermo dynamical reactions which occur at the fiber matrix interface during the process cycle, the thermal stresses induced during cooling from the process

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temperature and micro cracking in the fiber. Inter phase or matrix are all issues which need to be quantified. While there have been several previous and ongoing investigations to study the chemical/thermo dynamic reactions and thermal stresses which occur (see. for instance [Palmese. 1991] and [Sottos. 1990]. respectively), the current investigation will concern iwlf with microcracking.

In composites manufacturing, there typically exists a large difference in the coeficients of thermal expansion (CTE) between the reinforcement and matrix. Upon cooling from the process temperature, this may cause the formation of residual stresses which could be of sufficient magnitude to result in the formation of microcracks. These micro cracks can serve to degrade the mechanical performance of the composite, though interphases have been proposed to reduce the severity of the CTE mismatch [Misra. 1993].

Some composite systems designer have concluded will invariably contain microcracks [Kerans, Jero and Parthasarathy, 1994], therefore knowledge of how the interphase region influences and interacts with these microcracks becomes an important issue in the control of a composite's structural performance.

3. Research objective

The objective of this research is including;

Development of mechanics designing in composite material

Introduce the Linear Elastic crack Mechanics to evaluation of measure knowledge on the cracking behavior of composite materials.

 

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- Design for controlling damage with Examine the surface crack problem in a graded medium subjected to frictional sliding arbitrary profile.

4. Scope of the Study

The main focuses in this research is to Design for controlling damage with Examine the surface crack problem in a graded medium subjected to frictional sliding arbitrary profile.. As mentioned in this process some basic crack geometries in materials have been considered until now and some benchmark results are obtained. Also, several contact mechanics problems for graded materials have been solved to determine the stress field at the contact surfaces and to examine the effect of material non homogeneity on the contact stresses, but crack problems due to sliding contact have not yet been considered in literature. Since, the graded coatings are in most applications are composed of brittle ceramics, cracking under severe contact stresses is one of the most common failure modes (as shown in indentation and scratch tests).

Hence, it is also necessary to develop models that can predict subcritical crack growth behavior under contact loading and this requires the correct evaluation of the stress intensity factors for surface cracks.

5. Research structure

Structure of cracking sliding examination done that First, the problem of surface cracking in a homogeneous medium due to sliding contact is examined. Using the equations of elasticity for a homogeneous semi infinite medium the fracture and contact problems are formulated in coupled form

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and solved numerically to compute the mixed mode stress intensity factors and contact stresses. The exact elasticity formulation developed to formulate the crack/contact problem in a homogeneous medium is then extended to formulate crack and contact problems in a graded medium. First a surface crack problem in a graded material with known crack surface tractions is solved

6. Statement of the Problem

Some research explained that A semi-infinite crack is embedded normal to the interfaces in an otherwise infinite perfectly bonded biomaterial layered system consisting. This layered morphology may represent either a fiber-reinforced cross-ply laminate or a bimaterid periodically layered system. In this study, the materials for the two phases are taken to be homogeneous and linearly elastic. The cartesian coordinate system is chosen with its origin located at the crack-tip. The loading is assumed such that overall mode conditions prevail. The designing crack surfaces are traction free and the crack tip is assumed to be ideally sharp. Plane strain conditions are considered. For the analytical model, the crack-tip is assumed to be in the matrix phase at mid-distance between the adjacent interfaces. In formulating the near-tip finite element model, a cut-out region surrounding the physical crack-tip as indicated by the dashed lines will be considered.

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7. Overview of Crack Controlling Mechanism

In order to my proposal data collection that in recent years, designing graded crack in materials is proposed to be used as coatings or bulk materials to enhance the resistance of structural components to tribological damage. Failure in tribological applications results from high stresses at the contact surfaces and can occur in the form of cracking in brittle materials and plastic deformation in ductile materials. The main cracking patterns in brittle surfaces subjected to contact stresses are observed to be Hertzian cracking in spherical indentation and surface cracking due to frictional sliding contact. Multiobjective optimization problems with optimal designing have several objectives to be simultaneously optimized and sometimes some of objectives are conflicting. The difficulty in optimizing conflicting multiobjective problems is lack of the global optimum and existence of many local optimal areas as dimension increases. There may be no global optimum for the conflicting multi-objective problems. Considering in vector space, if all elements in a vector are optimal, the vector is considered as the global optimum.

8. Literature Review Previous Work

The first analysis of a design for controlling crack can be attributed to Muskhelishvilli (1963) who analyzed a circular an: cut using complex stress potentials. This type of crack was also investigated loaded in biaxial tension by Sih. Paris and Erdogan (1962) and in longitudinal shear by Sih (1965), However Cotterell and Rice (1980) note that the solution of Sih. Paris and Erdogan (1962) contained an error in the transcription of the solution and the

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correct expressions for the stress intensity factors of the circular an: crack can be found in [Cotterell and Rice. 1980].

The study of crack path prediction prompted the analysis of slightly curved cracks using first order approximations [Banichuk. 1970], [Goldstein and Salganik. 1974]. Cotterell and Rice report that these first order approximations are accurate to within 5% of the exact solutions for straight or circular are cracks when the local tangent angle at the tips of the slightly curved cracks differed by up to 15% from that of the straight or circular arc cracks [Cotterell and Rice. 1980]. Other investigations have utilized finite element analysis (FEA) to study the growth direction of a curved crack. Bergkvist and Guex (1979) investigated various crack propagation criteria and found that the trajectory of the curved crack is mostly independent of the choice of such criteria. These results were supported by the results of another FEA investigation of controlling cracks reported in [Ukadgaonker, Hargapurkar, and Maiti. 19881. Thermally driven curved crack growth in a brittle two-phase solid has been investigated using FEA in [Herrrnann and Grebner. 1982] and [Herrmann, 1987] who designed and found that crack growth in the direction of the principal stresses seemed to agree with experirnentai observations. Boundary element methods (BEM) have also been applied in the analysis of curved cracks [Smith and Mason. 19821.

9. Studies on the Design Process

Several experimental methods have been used for studying the design process and/or its associated cognitive activities. These include case studies, protocol studies, and controlled tests. There have been some studies in the past of designers working in teams. Christians studied individual industrial

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designers of varying creative levels and found differences in frequency of data collection and information processing in controlling of crack. There is not much reported on experimental studies of specific idea generation methods applied to engineering design, particularly groups engaged in conceptual design (except studies on Brainstorming or "free form" idea generation). Christians studied individual industrial designers of varying creative levels and found differences in frequency of data collection and information processing.

10. Analytical/Design Model

The development of the some previous model is based on the non-standard analysis approach of LVozniak for problems with periodic material microstructure and crack evaluation in them, wherein the displacements are postulated in terms of the homogenized displacements augmented by a family of kinematically admissible unit-cell local displacements. Here it is emphasized that the presence of geometrically non-periodic macrocrack does not violate any assumption used by Wozniak in formulating the non-standard analysis for micro-periodic material structure. In this approach, the local displacements are cast in terms of some unknown micromorphic functions and an a priori known unit-cell shape function. While the micromorphic parameters describe quantitatively the effects of the micro-periodic material structure, the shape function describes the expected qualitative character of these effects. The unknown micromorphic parameters are obtained by invoking an energy minimization technique. The homogeneous domain solution is then obtained by solving the Navier displacement field equations subjected to homogenized boundary conditions.

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11. Reference:

B. J. Dalgleish, K. P, and A. G. Evans, The strength and fracture of alumina bonded with alumhum alloys. Acta Metall., 37:1923-1931, 1989.

Beyerle, D. S., Spearing, S. M. and Evans, A. G. (1991). Dm-age mechanisms and the mechanical properties of a laminated 0.90 cerarnic/matrix composite. In press.

Chai, H. (1987). A note on crack trajectory in an elastic strip bonded by rigid substrates. Int. J. Fracture, 32,211.

Chai, H. (1988). Shear fracture. Int. J. Fracture, 37, 137.

Dvorak, G. J. and Laws, N. (1986). Analysis of first ply failure in composite laminates. Engng. Fracture Mech, 25,763.

D. Martinez and V. Gupta. Energy criterion for crack deflection at an interface between two ort hotropic media I1 Results and experimental verification. J. Mech. Phys. Solids, 42(8):MPS81, 1993.

D. L. Tullock, I. E. Reimanis, A. L. Graham, and J. J. Petrovic. Deflection and penetration of cracks at an interface between two dissimilar materials. Acta Metall. kfater., 42:3245-3252, 1994.

Dvorak, G. J. and Laws, N. (1988). Progressive transverse cracking in composite laminates. J. Composite Materials, 22,900.

Erdogan, F., 1995, "Fracture Mechanics of Functionally Graded Materials," Composites Ettgineering, Vol. 5, pp. 753 -770.

Fu, L., Khor, K.A., Ng. H.W., Teo, T.N., 2000, "Non-Destructive Evaluation of Plasma Sprayed Functionally Graded Thermal Barrier Coatings," Sztrj4ace and Coatings Technology, Vol. 130, pp. 233-239.

F. Erdogan and V. Biricikoglu. Two bonded half planes with a crack going through an interface. Int. J. Solids Structures, 11 (4):745-766, 1973.

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Fang, G. P., Schapery, R. A. and Weitsman, Y (1989). Thermal-induced fracture in composites. Engng. Fracture Mech, 33,619.

Freund, L. B. (1990). The driving force for gliding of a threading dislocation in a strained epitaxial layer on a substrate. $. Mech. Phys. Solids, 38,657.

Gille, G. (1985), Strength of thin films and coatings. In Current Topics in Materials Science, 12, E. Kaldis, ed. North Holland.

He, M. Y., Bartlett, A., Evans, A. G. and Hutchinson, J. W. (1991). Kinking of a crack out of an interface: Role of in-plane stress. J. Am. Ceram. Soc., 74, 767.

H. C. Cao and Evans A. G. On crack extension in ductilelbrittle laminates. Acta Metoll., 39:2997-3005, 1991.

H. E. Deve and M. J. Meloney. On the toughening of intermetallics with ductile fibers: the role of interfaces. Acta Metall., 39:2275-2284, 1991.

Hu, M. S., Thouless, M. D. and Evans, A. G. (1988). The decohesion of thin films from brittle substrates. Acta Met., 36, 1301.

Hutchinson, J. W. and Suo, Z. (1992). Mixed-mode cracking in layered materials. Advances in Applied Mechanics, 29,63.

Lu, T. C., Yang, J., Suo, Z., Evans, A. G., Hecht, R. and Mehrabian, R. (1991). Acta. Met. Muter. 39, 1883.

Parvizi, A., Garrett, K. W. and BAilet, J. E. (1987). Constrained cracking in glass fiber-reinforcement epoxy cross-ply laminates. J. Matter, Sci, 13, 195.

Suo, Z. (1990). Failure of brittle adhesive joints. Appl. Mech. Rev., 43, S276.

Shrawi. Mo, “Mechanics of Cracking for Composite Material”, PhD thesis, California University, 1992.

Timoshenko S. P. and Goodier J. N. (1970). Theory of Elasticity. McGraw-Hill, New York.

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Tada, H., Paris, P. C. and Irwin, G. R. (1985), The Stress Analysis of Cracks Handbook. Del Research, St. Louis, MO.

Wang, A. S. D. (1984). Fracture mechanics of sublaminate cracks in composite materials. Composite Tech. Rev., 6,45.

Ye, T., Suo, Z. and Evans, A. G. (1992). Thin film cracking and the roles of interface and substrate. Int. J. Solids Structures.

Zak, A. R. and Williams, M. L. (1963). J. Appl. Mech., 30, 142.

Zdaniewski, W. A., Conway, J. C. and Kirchner, H. P. (1987). J. Am. Ceram. SOC., 70, 104.


 



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