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Crack analysis by finite element method

Number of pages: 104 File Format: word File Code: 31462
Year: 2013 University Degree: Master's degree Category: Civil Engineering
Tags/Keywords: Crack growth patterns - Interlayer crack - leave - Leave the structure - Limited components - Sticky crack behavior pattern - Sticky crack pattern - Structural mechanics - structure - Turkish analysis
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  • Summary of Crack analysis by finite element method

    Master's Dissertation of Discontinuous Structure

    Abstract: In recent years, the use of composite material in the construction and strengthening of structures has expanded greatly. The structure of this material is such that there is a possibility of crack formation between the layers. Due to the increase in load, these cracks grow and cause a severe drop in the strength and hardness of the structure. Applying numerical methods in this field and obtaining answers plays an important role in estimating Turkish behavior. The initiation and expansion of the interlayer fracture in the composite material are performed with numerical fans. In this method, the adhesive components are used together with the characteristic behavior diagram of the material and crack growth is investigated. It is noted that a suitable material behavior diagram is effective in improving the response of s. Therefore, a component is proposed and used in numerical examples and its characteristics are evaluated. The correctness of the answers in the interlayer failure of the composite material will be verified with a numerical method. Numerical examples reveal that the proposed adhesive component with a small number of analysis gives the answers with good accuracy.

    Key words: composite material, interlayer crack failure and propagation, adhesive crack behavior pattern, behavior function, adhesive component.

    Chapter 1

    The beginning of the speech

    1-1- Preface

    One of the important reasons for the failure and collapse of structures is the existence of the first cracks and their expansion. These cracks are mostly caused by various factors, and among them, errors in the process of building the structure, operating loads, and the like. The presence of cracks in different shapes and sizes creates different behaviors in the structure. Some of these cracks do not affect the function of the structure, while others expand and lead to its sudden failure. So far, many costs have been paid due to the failures caused by the crack. By choosing the right solution, the costs can be greatly reduced. On the other hand, accurate estimation of damage rate and structure life is required in structures with high reliability. Based on the importance of the construction goals, the sensitivity of the risks and damages caused by the structural failure, the prediction of the place of occurrence of the crack and the direction of its expansion are considered important points in the design and analysis of structures.

    In recent years, the use of new materials in the construction and strengthening of structures has been very impressive. Accurate understanding of the behavior of the composite material leads to an optimal design. In addition to many advantages, there are also some shortcomings in modeling the behavior of this material. Among them, we can mention how Turkey broke and expanded. It should be known that structural failure analysis is only possible in few cases explicitly. Therefore, numerical methods have found a special place in investigating the fields of crack and failure. So far, a wide range of numerical methods have been used to solve the failure problem.  In this research, the numerical investigation of interlayer fracture in the composite material is discussed.

    1-2- Crack growth patterns

    In investigating the phenomenon of fracture and crack propagation, the analyst is faced with complex behavioral processes of the material. These processes can be divided into three behavioral steps: first, the creation of hair holes and cracks in several points of the body, then the growth of the holes and their interaction and joining. These actions lead to the formation of large cracks. Then, the growth and propagation of cracks destroy the structure [G1].

    With the help of an efficient numerical method, together with a suitable behavioral model that simulates the effect of the crack in the material, the failure phenomenon in the material can be investigated. The simplest model used in failure analysis is the linear elastic model. Based on this, the behavior of the material at the edge of the crack is considered to be elastic and linear. Although this assumption leads to unrealistic results, such as infinite stress at the edge of the crack, it has been widely used in many researches [s1]. Nevertheless, various models are also available to make the prediction of failure behavior more realistic. Among them, two behavior patterns, sticky and failure, have attracted more attention. In the adhesive solution, the crack effect is simulated only in a certain area. This technique is very interesting due to its simplicity of application in finite element method programs [B2].. In the failure method, by introducing the failure factor in a continuous environment, the crack effect is introduced on a part of the domain.  The effect of encountering the failure rate and the effect of the material's behavior is the main part of this failure method [K1]. 1-3 Cracks in the composite material Composite material is formed from two or more materials. Its purpose is that the performance and characteristics of the composite material are superior to the characteristics of each of them alone. By choosing the desired number and proper orientation of the threads in the field, it is possible to spread the tension and change the direction of the load. On the other hand, the layered structure of the composite material is such that the crack formation occurs between the layers. These cracks can grow due to the load and cause a severe drop in the strength and hardness of the structure. The appearance of interlayer cracks can be caused by the deficiency of the first material, free edge stresses, impact and so on. It is possible to estimate the origin of the crack and how it spreads by using numerical and laboratory methods. Due to spending a lot of money and time to perform complex experiments, numerical analyzes are superior. For nodes in that section, the crack growth criterion is checked. In the nodes where the crack growth criterion is established, the crack is slightly pushed forward and the process is repeated. This method continues until the crack surface is obtained after establishing growth conditions in all the nodes on it.

    In this research, two numerical methods of crack patterning and its expansion in the composite material are investigated. First, by using the four-node components and choosing the release value of the strain function, for the crack growth criterion, crack simulation and its expansion is done. In the second method, adhesive components will be used. Crack behavior is introduced with the help of sticky function relation. By choosing the optimal function for the proposed adhesive component, a behavior very close to reality can be achieved. The correctness of the analysis answers is evaluated with the help of the proposed component with the first method. The accuracy of the answers in the minimum number of analyzes shows that the proposed adhesive component works well in modeling the interlayer failure of the composite material.  

     

    1-4- Dissertation organization

    This thesis has seven chapters. What followed was the opening chapter of this article and an introduction to the topic of the research. The second chapter describes various behavior patterns in the simulation of leaving and its expansion. The formation and growth of the interlayer crack in the composite material will be examined in the third chapter. In the fourth chapter, the simulation of the crack and its growth in the composite material is described. There, the release value of the strain factor for the crack growth criterion and various ways of finding it are introduced.  In recent years, in order to achieve a behavior closer to reality, in the simulation of the interlayer crack and its propagation in the composite material, adhesive components are used. In the fifth chapter, the adhesive component and its relationship in the finite element method as well as the crack growth criterion come. This research, using the relationships that govern the behavior of the adhesive component, examines the most suitable function in estimating the interlayer crack behavior in the composite material. The improvement of the behavior of the structure with the proposed adhesive component is the result of the work. In other words, taking advantage of this component is effective in obtaining more accurate answers. In the sixth chapter, the correctness of the author's method is revealed by using the suggested component in the samples of the sign stone. Finally, suggestions for future researches will come in the final chapter.

     

     

     

    Chapter Two

     

    Patterns of Quit Growth

     

    2-1- Preface

    Various patterns can be used based on quit behavior. win The choice of each method has an effect on the behavior of the Turkish variables.  There are three main fan for this: linear elastic behavior, adhesive crack and failure pattern. In the rest of this chapter, the description of each of these will be discussed.

    2-2- Linear elastic behavior

    For the first time, this model was used to investigate the behavior of structures with cracks. In this way, they considered the cracked material to have linear and elastic behavior. Griffis and Inglis conducted the first analytical research in the 1920s in the field of Turkish simplification [G1, I1]. They obtained singular values ??of stress at the crack edge. After that, the finite element method was used to investigate such behaviors. In this regard, Chen showed that polynomial form functions in components cannot model singular behavior [C1]

  • Contents & References of Crack analysis by finite element method

    List:

    Abstract. An

    index of figures. Five

    Index of tables. No

    Chapter 1: The beginning of speech. 1

    1-1- Preface 1

    1-2- Turkish growth patterns. 2

    1-3- cracks in the composite material. 2

    1-4- organizing the thesis. 3

     

    Chapter Two: Turkish growth patterns. 6

     

    2-1- Preface 6

    2-2- Linear elastic pattern. 6

    2-3- adhesive crack pattern 7

    2-4- failure behavior pattern. 8

    Chapter three: The failure of composite matter. 9

    3-1- Preface 9

    3-2- Compound substance. 10

    3-3- mechanical behavior of composite material. 10

    3-4- Stress and strain dependence of material 10

    3-5- Fracture in composite material. 16

    3-6- Interlayer crack formation. 18

    3-6-1- Separation of layers of composite material. 20

    3-6-2- Free edge stresses 20

    3-6-3- Impact. 21

    3-7- Growth of interlayer cracks. 21

    Chapter four: Crack growth in composite material. 23

    4-1- Preface 23

    4-2- Criterion of crack growth in composite material. 23

    4-3- Finding the release value of the strain function. 24

    4-3-1- Beam angle 25

    4-3-2- Area method. 27

    4-3-3- The solution of virtual expansion of Turkey. 28

    4-3-4- the fan of the primary function independent of the path. 29

    4-3-5- method of virtual closure of Turkey. 32

    Chapter Five: Adhesive contact component 35

    5-1- Preface 35

    5-2- Adhesive component 35

    5-3- Relation of adhesive crack pattern 38

    5-3-1- Relation of two-line adhesive pattern. 40

    5-4- Correlation of adhesive function 42

    5-4-1- Examining the stress-strain diagram. 42

    5-4-2- Relation of elastic function. 44

    5-4-3- Linear elastic function. 45

    5-4-4- quadratic parabolic elastic function 46

    5-4-5- power elastic function. 46

    5-4-6- Logarithmic elastic function. 47

    5-4-7- Comparison of the proposed elastic functions. 47

    5-5-Finite component method of adhesive area 49

     

    Sixth chapter: Interlayer fracture tests. 51

    6-1- Preface 51

    6-2- The method of virtual closing of Turkey. 51

    6-3- Simulation by adhesive component method 52

    6-4- Numerical samples. 53

    6-4-1- double tower beam. 54

    6-4-2- One part bending sample. 62

    6-4-3- Example of a cracked bending beam 66

    Seventh chapter: the end of the speech. 76

    1-1- Preface 76

    7-2- Thesis excerpt. 76

    7-2- Conclusion. 77

    3-7- Future researches. 77

    Handbooks 78

    Persian to English dictionary. 84

    Nomenclature 86

     

     

    Source:

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    ]p.1 [- Sadeghi, Yaser, Relation of bending plate Smart Multilayer, Master's Dissertation of Discontinuous Structures, Ferdowsi University of Mashhad, 1389

    ]A1[- Ain Afshar, Atefeh, Bending analysis of circular and rectangular composite multi-layer elastic plates with different geometrical characteristics by dynamic release method, Master's Dissertation of Discontinuous Structures, Ferdowsi University of Mashhad, 1385.

    [A1]-Armero F, Oller S. A General Framework for Continuum Damage Models. I. Infinitesimal Plastic Damage Models in Stress Space. Int. J. Solids Structs. 37(2000), pp.7409-7436.

     

    [A2]-Alfano G., Crisfield M.A., Finite element interface models for the delamination analysis

    of laminated composites: mechanical and computational issues, Int. J. Numer. Methods

    Engng. 77(2) (2001): 111-170.

    [B1]-Barsoum R.S. On the use of isoparametric finite elements in linear fracture mechanics. Int J Num Meth Engng. 10(1976), No.7, pp.25-37.

    [B2]-Barenblatt GI. The formation of equilibrium cracks during brittle fracture general ideas and hypotheses. J Appl Math Mech. 23(1999), No.4, pp.622-633.

    [B3]-Bouchard P.O, Bay F,O, Bay F, Chastel Y. Numerical modeling of crack propagation: automatic remeshing and comparison of different criteria.  Comput. Methods Appl. Mech. Engrg. 192(2003), pp.3887-3908.

    [B4]-Bouchard P.O, Bay .F, Chastel .Y. Numerical modeling of crack propagation: automatic remeshing and comparison of different criteria. Comput. Methods Appl.Mech.Engrg.192(2003), No.8, pp.3887-3908.

    [B5]-Bishop S.M., Dorey G. The Effect of Damage on the Tensile and Compressive Performance of Carbon Fiber Laminates. AGARAD conference proceedings, (1983) No.335.

    [B6]-Bishop S.M. A Review of the Strength and Failure of High Performance Woven Carbon Fiber Reinforced Plastics. (1986) UK.

     

    [B7]-Bishop S.M. The Mechanical Performance and Impact Behavior of Carbon-Fiber Reinforced. Composite Structures,13(1985),pp 295-318.

    [B8]- Burlayenko V.N, Sadowski T. FE modeling of delamination growth in interlaminar fracture specimens. Budownictwo i Architektura 2 (2008) 95-109.

    [C1]-Chan .SK, Tuba IS , Wilson WK. On the finite element method in linear fracture mechanics. Engng Fracture Mech. 45(1970), No.6, pp.967-973.

    [C2]- Chandra .N, Li .H, Shet .C, Ghonem .H. Some issues in the application of cohesive zone models for metal-ceramic interfaces. Int J Solids Struct.39(2002), No.8, pp.2827-2855.

    [C3]-Cui .W , Wisnom .M.R. A combined stress-based and fracture-mechanics-based model for predicting delamination in composites. Composites.24(2004), No.9,pp.74-467.

    [C4]-Cordebois JP, Sidoroff F. Endomagement Anisotrope en Elasticité et Plasticité.Journal de Mécanique Théorique et Appliquée.(1982). pp.45-60.

     

    [C5]-Camacho. G.T., Ortiz. M. Computational modeling of impact damage in brittle materials. Int J Solids Struct. 33(1996), No.6, pp.2899-938.

    [D1]-Dugdale .D.S. Yielding of steel sheets containing slits. J Mech Phys Solids. 8(2006), No. 9, pp.100-114. [E1]-Erdogan .F, Sih .G.C. On the extension of plates under plane loading and transverse shear. J Basic Engng, ASME. 85(1996), No.4, pp.519-527. [E2]-Espinosa, H.D., Zavattieri, P.D. A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: Theory and numerical implementation". Mech Mater.35(2003), No.7, pp.333-364.

    [F1]-Feih S. Development of a user element in ABAQUS for modeling of cohesive laws in composite structures. Ris?-R Report. National Laboratory Roskilde Denmark. January 2005.

    [G1] - The phenomena of rupture in solid. pp.589-602.

    [G3]-Continuum Theory of Void Nucleation and Growth.J. Eng. Mater.Tech. 99(2006),No. R.D. Crack tip are unnecessary. 90(1975) , 495-507. Philadelphia.(1994), pp.2-28.

    [H3]-Hillerborg .A, Modéer .M, Petersson .P. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res. 6(2006), No.6, pp.773-782.

    [H4]-Hirakovich C.T. Influence of Layer Thickness on the Strength of Angle Ply-Laminates. J. of composite materials, 16(1982), No. 3, pp. 216-227. [H5]-Halpin J.C. Primer on Composite Materials. Technomic Company, 1984.

    [H6]-Hellen T.K

Crack analysis by finite element method
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