Effect of sharp edges on stress value via fea Essay Example

Effect of sharp edges on stress value via fea Essay Example Effect of sharp edges on stress value via fea Essay Effect of sharp edges on stress value via fea Essay ( 1 ) Introduction STRESS INTENSITY FACTOR: A major accomplishment in the theoretical foundation of LINEAR ELASTIC FRACTURE MECHANICS ( LEFM ) was the debut of the emphasis strength factor K. It is the parametric quantity used to gauge the strength of emphasiss near to the cleft tip and related to the energy release rate ( Bazant and Planas 1998 ) . Ingliss ( 1913 ) studied the unexpected failure of naval ships, and Griffith ( 1921 ) extended this work utilizing thermodynamic standards. Using this work, Irwing ( 1957 ) developed the construct of the emphasis strength factor. Stress strength factors shows the step of the alteration in emphasiss within the vicinity of the cleft tip. Therefore, it is of import to cognize that in which way the cleft is turning and when the cleft stops propagating. The emphasis strength factor is compared with the critical emphasis strength factor KIC ( the capacity ) to find whether or non the cleft will propagate. ( 2 ) STRESS INTENSITY FACTOR AND CRACK TIP STRESSES A uniqueness of 1/Sqrt ( R ) is produced by cleft tips. The emphasis Fieldss near a cleft tip of an isotropic additive elastic stuff can be expressed as a merchandise of 1/Sqrt ( R ) and a map of theta with a grading factor K: inferiors I, II, and III are 3 different types of lading applied on a cleft. Where K= emphasis strength factor ( 3 ) MODES OF LOADING Manner I ( Tensile Opening ) Mode II ( In-Plane Shear, Sliding ) Mode III ( Ot of Plane Shear, Tearing ) For all the three types of lading the emphasis Fieldss and the supplanting Fieldss around the locality of the cleft tip are individually written Grecian missive is know as shear modulus and is depicted as G, and it should non be mistaken for the strain release rate, .Formulas for plane emphasis and plane strain are: The rule of superposition is applied for additive elastic stuffs. So the look obtained is: ( 4 ) STRESS INTENSITY FACTOR IN PRACTICE: The most interested country for applied scientists is the emphasis in the vicinity of cleft tip and look into whether the value is more than the break stamina. Thus K is the map of sigma for any given R and theta. For case the K for following specimen is The dimension of K is The different solutions of K for three classs: authoritative, specimen, and construction are: Infinite Plate with a Center Through Crack under Tension Single Edge Notched Specimen Under Bending ( 5 ) STRESS INTENSITY FACTOR AND FRACTURE TOUGHNESS The additive elastic break mechanics theory says that there is infinite emphasiss at the tip of the cleft but really fictile zone is developed near the cleft tip that opposes the emphasiss to some definite values. It is instead impossible to measure the right sum of emphasiss in this plastic zone and associate them to the maximal allowable emphasiss of the materialto justice the behaviour of the cleft. Critical emphasis strength factor Kc of any stuff can be obtained by figure of experiments and this promotion is called the break stamina. Thus the behaviour of the cleft can be predicted by comparing K and Kc straight. Kc s for a figure of common technology stuffs are listed in this page. RELATIONSHIP BETWEEN G and K Sometimes energy release rate G can besides be used alternatively of stress strength factor K. But both the parametric quantities are inter related to each other and is shown below: The dimension of is ( 6 ) Influence OF STRESS INTENSITY FACTOR ( K ) The cleft extension in any specimen depends on the magnitude and rate of alteration of K. A graph can be plotted of cleft growing with regard to lade rhythm against the different K at that peculiar point for any specimen. Sing strictly elastic conditions thorough cognition of emphasis and strain field near the vicinity of cleft tip can be modulated and estimated with the aid of stress strength factor. As the fictile field is created near the cleft tip the truth of the emphasis calculated is reduced. Brittle material gives more precise replies for emphasis strength factor is besides every bit compared to ductile stuffs because malleable stuffs tend to deform before failure. Fracture mechanics uses stress strength factor ( K ) to foretell and estimeate the emphasiss near the cleft tips more accurately, due to lading and residuary emphasiss. When this stresses reaches the critical value a cleft starts turning and finally consequences in the failure of stuff. The break strength can be defined as the failure occurred at a peculiar load..At foremost the clefts are really little and can non be seen but later it consequences in the failure of the stuff if non known. Unlike stress concentration , Stress Intentsity, K, chiefly focusses on the magnitude of the applied emphasis which includes the type of load.. The three different types of burden are Mode-I, -II, or -III. KIc of 1st type of burden is the most of import and most parametric quantity which is normally used in the field of technology in break mechanics and hence must be understood so that break defying stuffs can be used in the designing of assorted edifices, aeroplanes, Bridgess, etc. Infact we can state that if the cleft is seen, it means the emphasiss are really near to the optimal values as estimated by Stress Intensity Factorfor most of the stuffs. ( 7 ) STRESS ANALYSIS OF CRACK Brittle breaks are the most concerned country for applied scientists as the toffee fractures brings the most risky accidents and happens really rapidly, and normally the failure in brickle stuff are caused because the applied stresses reaches its critical bound value near the locality of cleft tip. K can be used to specify the break stamina as: where Y is a dimensionless parametric quantity and depends on both the constituent type and the geometry followed by the cleft. Normally, cleft which has egg-shaped form the equation is modified and uses three different Y s to include ace geometry: Takin the cleft length into considerations if the thickness of the geometry is really big, the emphasis strength factor for field strain break stamina can be estimated which include the geometry of the specimen and output strength. Thus the thickness of the specimen is the most impotant parametric quantity which controls the passage of break stamina from plane emphasis to shave strain , Stress and supplanting Fieldss near a cleft tip of a additive elastic isotropic stuff are listed individually for all three manners: ModeI, ModeII, ModeIII. The Grecian missive denotes the shear modulus, normally written as G, and it should non be mistaken for the strain release rate, .Formulas for plane emphasis and plane strain are: The rule of superposition is applied for additive elastic stuffs. So the look obtained is: ( 8 ) Case STUDY: Let us take the illustration of a specimen with a V notch holding four point crook burden. Harmonizing to break mechanic theory, the theoretical emphasis strength factor for a four point crook beam ( figure B.1 ) is calculated with the undermentioned equation K= ( 3Pl/tw^2 ) * ( pi*a ) ^.5* ( 1.122-1.121 a+3.740 a^2+3.873 a^3-19.05 a^4+22.55 a^5 ) where, a is the cleft length, W is the breadth of beam, P is the burden applied, cubic decimeter is the distance between the axial rotations, t is the thickness of specimen and W a= a /w The dimensions, material specification and trial constellation of the four point flexing specimen are shown: . Parameters DIMENSIONS ( W ) 11.4 millimeter ( T ) 2.9 millimeter ( s ) 70 millimeter ( cubic decimeter ) 20 millimeter ( vitamin D ) 30 millimeter ( a ) 3.6 millimeter ( P ) 1000 millimeter The different values of K calculated for different values of cleft length is show in the undermentioned tabular array Analytic computation of the Stress Intensity Factor ( K ) : Based on the values the graph has been plotted for emphasis strength factor agains ace length. The graph shows that as the cleft length increases the emphasis strength factor additions. ANALYSIS VIA FEA The burden and restraints are same for all the three readings. merely the mesh relevancy has been changed. Tonss and Constraints The undermentioned tonss and restraints act on specific parts of the portion. Regions were defined by choosing surfaces, cylinders, borders or vertices. Table 3 Load and Constraint Definitions Name Type Magnitude Vector Force 1 Edge Force 500,0 N 0,0 N -500,0 N 0,0 N Force 2 Edge Force 500,0 N 0,0 N -500,0 N 0,0 N Fixed Constraint 1 Edge Fixed Constraint N/A Unconstrained 0,0 millimeter Unconstrained Fixed Constraint 2 Edge Fixed Constraint N/A Unconstrained 0,0 millimeter Unconstrained Table 4 Constraint Chemical reactions Name Force Vector Moment Moment Vector Fixed Constraint 1 500,0 N 0,0 N 500,0 N 0,0 N 1,636e-010 NAÂ ·mm 1,636e-010 NAÂ ·mm 0,0 NAÂ ·mm 0,0 NAÂ ·mm Fixed Constraint 2 500,0 N 0,0 N 500,0 N 0,0 N 2,529e-010 NAÂ ·mm 2,529e-010 NAÂ ·mm 0,0 NAÂ ·mm 0,0 NAÂ ·mm Geometry and Mesh ( 1 ) The Relevance scene listed below controlled the choiceness of the mesh used in this analysis. For mention, a scene of -100 produces a harsh mesh, fast solutions and consequences that may include important uncertainness. A scene of +100 generates a all right mesh, longer solution times and the least uncertainness in consequences. Zero is the default Relevance scene. Table 1 Arpit_0 Statisticss Jumping Box Dimensions 100,0 millimeter 11,4 millimeter 2,9 millimeter Part Mass 2,58e-002 kilogram Part Volume 3287 mmA? Mesh Relevance Setting -3 Nodes 543 Consequences The tabular array below lists all structural consequences generated by the analysis. The undermentioned subdivision provides figures demoing each consequence contoured over the surface of the portion. Safety factor was calculated by utilizing the maximal tantamount emphasis failure theory for malleable stuffs. The emphasis bound was specified by the tensile output strength of the stuff. Table 2 Structural Consequences Name Minimum Maximum Equivalent Stress 0,1422 MPa 267,4 MPa Maximal Principal Stress -3,658 MPa 322,5 MPa Minimal Principal Stress -267,6 MPa 28,94 MPa Distortion 1,283e-003 millimeter 0,105 millimeter Safety Factor 0,935 N/A Geometry and Mesh ( 2 ) Table 5 Arpit_100.ipt Statisticss Jumping Box Dimensions 100,0 millimeter 11,4 millimeter 2,9 millimeter Part Mass 2,58e-002 kilogram Part Volume 3287 mmA? Mesh Relevance Setting 100 Nodes 1115 Consequence Table 5 Structural Consequences Name Minimum Maximum Equivalent Stress 3,423e-002 MPa 292,1 MPa Maximal Principal Stress -9,596 MPa 352,5 MPa Minimal Principal Stress -262,0 MPa 20,94 MPa Distortion 2,115e-003 millimeter 0,1066 millimeter Safety Factor 0,8559 N/A ( 9 ) Decision It can be seen that for the same burden and and all other parametric quantities the maximal emphasis is developed at the cleft tip. But the value of the maximal tantamount emphasis is non the same in the two figures. The emphasiss possess uniqueness near the locality of cleft tip. As a consequence, the emphasis value will depend on FEA mesh size.The finer the mesh, the higher the emphasis. You will neer acquire converged consequences utilizing stress standards This is because FEa tends to average the value at that peculiar point and we get some value. So if we increase the mesh the emphasis value will travel higher. Thus the more refined the mesh is more realistic value we get. As the cleft part is in plastic zone so we get infinity value for emphasis theoretically but we get some definite value via FEA. Thus the specimen is checked by experimentation to see when the cleft is formed and when it reaches the critical value so that any farther usage will ensue in the failure of the constituent ( 10 ) Mentions 1. www.efunda.com 2. Beevers, C, J- Advavces in cleft length measuring 1982 3. Hertzberg, W, Richard- Deformation and Fracture of engg. Metallic elements 4. 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