![Simulation of Critical Crack Length Propagation…
www.ijceronline.com Open Access Journal Page 64
III. CONCLUSION
Initially data collection and literature survey was done on critical length on various materials.
By analysis in three materials aluminum has high strength and life cycle and damage will be less compared to E-
glass epoxy material.
In aerospace design epoxy’s are widely used to make outer body’s, these outer bodies caused to damage with
small hit or crack initiation so better to use mixture of aluminum and carbon mixture in good qualities.
IV. FUTURE SCOPE
Epoxy materials are not able to withstand after crossing safe zone (initiation of crack). When we mix the
aluminum materials and E-glass epoxy material the material can with stand and life cycle of material can be
increased.
REFERENCES
[1] G. Fajdiga and M. Sraml; Fatigue Crack Initiation and Propagation under Cyclic Contact Loading.
[2] Mr. Quinton Row son consultant Structural Integrity, Quest Integrity NZL Ltd., New Zealand Mr. Michael Rock engineering
Project Manager, Mighty River Power Ltd., New Zealand; Comparison between ductile tearing analysis and linear elastic
fracture mechanics analysis.
[3] Donoso, J.R. and Landes; Materials Science Department, Universidad Tecnica Federico Santa Maria Valparaiso, CHILE
juan.Donoso@Usm.Cl
2
MABE Department, The University Of Tennessee Knoxville, TN Usalandes@Utk.Edu;An instability
analysis for a crack growth situation based on the common format.
[4] fracture and fatigue crack growth analysis of rail steels; Journal Of Mechanics Of Materials And Structures
[5] M kulkarni1, Ravi prakash2 and A N kumar3; Experimental And Finite Element Analysis Of Fracture Criterion In General
Yielding Fracture Mechanics
[6] H. Sun, S. Rajendran and D. Q. Song: Finite Element Analysis on Delimitation Fracture Toughness Of Composite Specimens
[7] Tipple and G. Thorwald; Using the Failure Assessment Diagram Method with Fatigue Crack Growth To Determine Leak-Before-
Rupture.](https://image.slidesharecdn.com/j064058064-160916064609/85/Simulation-of-Critical-Crack-Length-Propagation-Using-Fracture-Mechanics-7-320.jpg)
Simulation of Critical Crack Length Propagation Using Fracture Mechanics
- 1. ISSN (e): 2250 – 3005 || Volume, 06 || Issue, 04||April – 2016 || International Journal of Computational Engineering Research (IJCER) www.ijceronline.com Open Access Journal Page 58 Simulation of Critical Crack Length Propagation Using Fracture Mechanics Mr.DEGALA RAJENDRA1 , Mr. P RAVICHANDER2 /Prof. R V PRASAD3 1 Sri Padmavathi Mahila University, Technology Tirupati 2,3 Methodist College Of Engineering & Hyderabad I. INTRODUCTION Basically metal plates cause to fatigue cracks when it crosses its yield strength limit casually ,all the materials withstands up to 10+7 (cycles) this is called as safe zone limit 10+8 to 10+10 (cycles) is called critical zone. Most failures occur in materials are selection of proper material, processing, manufacturing procedures, incorrect usage. When the material is imposed of stresses, stress fracture of material can be two or more pieces. Types of failure: Failures of material are of two types, they are: Buckling and Fracture. Buckling: When the material is subjected to a compressive load, buckling causes a lateral bend in the material. Buckling results failure of material within the catastrophic failure. Types of fracture: In fracture failures Physical separation, or tearing of the material, through either an internal or external crack. Fracture of material are two types, they are: Ductile and Brittle fracture. Ductile and brittle fracture Fracture occurs due to stress concentrations at flaws like Surfaces scratches(stamp marks, inspection marks, surface irregularities), Variation in material properties(blow holes, cavities, weld strikes, and foreign inclusions )Discontinuities in the component(holes, grooves, keyways, screw threads and Abrupt changes in cross section (gears, sprockets, pulleys, ball bearings, splines on shafts) Ductile fracture: Ductile fracture materials are calculated by depending on momentum of the material. In Ductile fracture large amount of plastic deformation takes place before the fracture. Slow propagation and absorption of large amount energy is observed before the fracture. In ductile materials, particularly in high purity materials can with stand up to 50-100% large deformation or more strain before fracture under loading condition. Ductile fracture mostly influenced by: Transition temperature, inclusions, and strain hardening. Brittle fracture: Brittle fracture materials are calculated by depending on strength of the materials. In Brittle fracture small amount of plastic deformation takes place before the fracture. In brittle materials, particularly in brittle crystalline materials fracture can occur due to the result of tensile stress acting normal to crystallographic. Brittle fracture mostly results in catastrophic failure of a structure. Brittle fracture mostly influenced by: Defects, fatigue, and stress-corrosion. ABSTRACT The focus of this paper is to investigate and analyze the study on the plate of steel, Aluminum and Epoxy with a center crack. Linear elastic fracture mechanics principles have been used for calculating Stress Intensity Factor, Critical crack length, Increment in crack, Mean stress and strain Amplitude at critical fatigue load cycles. Above calculations will be done on the plate with centre crack of various materials (steel, aluminum and epoxy) to predict crack length to evaluate and to compare the results with theoretical calculations. .Conclusions/results obtained on the basis of analysis. Keywords: FRACTURE MECHANICS,FEM,ANSYS
- 2. Simulation of Critical Crack Length Propagation… www.ijceronline.com Open Access Journal Page 59 Fatigue failures: Fatigue means weakening of materials by applying repeated loading and unloading. When the material is subjected to cyclic loading, progressive and localized structural damage occurs in material. The nominal maximum stress values that cause such damage may be much less than the strength of the material typically quoted as the ultimate tensile stress limit, or the yield stress limit. If the loads are above a certain threshold, microscopic cracks began to form at the stress concentrators such as surface, persistent slip bands (PSBs), and grain interfaces. Eventually crack will reach a critical size, the crack will propagate suddenly, and structure will fracture. The shape of the structure will significantly affect the fatigue life; square holes or sharp corners will lead to elevated local stresses where fatigue cracks can initiate. Round holes and smooth transitions or fillets will therefore increase the fatigue strength of the structure. Low Cycle Fatigue: Low cycle fatigue involves less numbers of cycles (N1000), Failure of Set screws, short lived devices like missiles. High cycle fatigue: High cycle fatigue involves a large number of cycles (N4105 cycles) and an elastically applied stress. High cycle fatigue tests are usually carried out for 10+7 cycles sometimes 10+8 cycles for nonferrous metals. Although the applied stress is low enough to be elastic, plastic deformation can take place at the crack tip. Failure of Springs, ball bearings, gears subjected to fluctuating stresses. High cycle fatigue data are usually presented as a plot of stress, S, Vs the number of cycles to failure N. along scale is used for the number of cycles. The value of stress, s, can be the maximum stress, S max, the minimum stress, S min, or value of mean stress, S m, or one of the two ratios, R or A. The fatigue life is the number of cycles to failure at a specified stress level, while the fatigue strength (also referred to as the endurance limit) is the stress below which failure does not occur. As the applied stress level is decreased, the number of cycles to failure increases. Normally, the fatigue strength increases as the elastic tensile strength increases. II. EXPERIMENTAL ANALYSIS Nomenclature A fracture = cross-section of the specimen at fracture. A 0 = initial cross-section of the specimen. C = fatigue ductility exponent. E = young’s modulus. N = describe the relative position of the crack tip to the grain boundary. N f = number of load cycles to failure. δ l ƒ = fatigue strength coefficient. Є fracture = specific deformation of the specimen at fracture. δЄ = specific deformation increment. δ l f = fatigue ductility coefficient. δ uts = ultimate tensile strength INPUTS FOR STEEL AISI: A fracture = 5.89 A = 6 C = 3 E = 180Gpa N = 2
- 3. Simulation of Critical Crack Length Propagation… www.ijceronline.com Open Access Journal Page 60 N f = 10 8 δl f = 2.8 Є fracture = 2.03735 δ ι ƒ = 106 δ uts = 400mpa Critical crack length calculation: Fatigue crack initiation: = =55.55*1.04+2.8*1.066 =56.59+3.866 =60.456 Strain amplitude: Marrows ( - N) method According to coffin-Manson =2*1.0186 =2.03735 1.75*2.2-3 *0.083176+0.5*1.53263*3.98-6 =0.01367+2.177-4 Strain =0.0138 Mean stress Smith Watson Topper Method = 8169643.74+235877379.9 =317575023.4 Pascal’s =317.5Mpa INPUTS FOR ALUMINUM A fracture = 5.89 A0 = 6 c = 3 E = 74.5Gpa N = 2 N f = 108 δ l f = 104 Є fracture = 2.03735 δ l f = 3.2 δ uts = 168mpa
- 4. Simulation of Critical Crack Length Propagation… www.ijceronline.com Open Access Journal Page 61 Critical crack length calculations: Fatigue crack initiation1 : = =0.1394+3.3888 =3.528 Strain amplitude: Marrows method According to coffin-Manson =2*1.0186 =2.03735 =4.3270×10-4 +1.2145×10-5 =0.004448 Strain = 0.004448 Mean stress: Smith Watson Topper Method = =7281310.163+2883.267 =7284193.43 Pascal’s =72.84Mpa INPUTS FOR EPOXY A fracture = 5.89 A o = 6 c = 3 E = 30Gpa N = 2 N f = 108 δ l f = 107 Є fracture = 2.03735 δ l f = 2.1 δ uts = 550mpa Critical crack length calculations: Fatigue crack initiation: = =346.3225+2.2239 =348.54
- 5. Simulation of Critical Crack Length Propagation… www.ijceronline.com Open Access Journal Page 62 Strain amplitude: Marrows method According to coffin-Manson =2*1.0186 =2.03735 =3.5300×10-3 Strain = 0.0035 Mean stress: Smith Watson Topper Method = =7214723960 Pascal’s=721.84Mpa RESULTS TABLE Theoretical STEEL AIST 1504 ALUMINUM E-GLASS EPOXY specific deformation increment Strain amplitude 2.03735 2.03735 2.03735 Strain 0.0138 0.004448 0.0035 Mean stress 317.5Mpa 72.84Mpa 721.84Mpa Analysis results with 10x cycles STEEL AIST 1504 ALUMINUM E-GLASS EPOXY DISPLACEMENT 0.32605 0.92594 0.87737 STRAIN 0.0086302 0.0240 0.02459 STRESS 1726 1710.2 1781 LIFE 62.39 to 1e6 0 to1e8 57.949-1e6 DAMAGE 1000 to1.602e7 10 to1e32 1000 to 1.7257e7 FACTOR OF SAFTY 2.845 2.832 2.58 BI-INDICATION 0.99891to0.966 0.993 to 0.97666 0.99 to0.867 ALL-STRESS 1726 1710.2 1781 MODE 1 341.51 1631.8 1725.5 MODE 2 632.86 2939.1 3086.6 MODE 3 1540.8 3033.4 3122.7 MODE 4 2853.6 3663.6 3731.6 MODE 5 3132.4 4577 4772.7 MODE 6 3537 5615.1 5779.6
- 6. Simulation of Critical Crack Length Propagation… www.ijceronline.com Open Access Journal Page 63 STEEL AIST 1504 Analysis DISPLACEMENT 0.32605 STRAIN 0.0086302 STRESS 1726 LIFE 62.39 to 1e6 DAMAGE 1000 to1.602e7 FACTOR OF SAFTY 0.049to2.845 BI-INDICATION 0.99891to0.966 ALL-STRESS 1726 MODE 1 341.51 MODE 2 632.86 MODE 3 1540.8 MODE 4 2853.6 MODE 5 3132.4 MODE 6 3537 Mean stress ALUMINUM Analysis 10x DISPLACEMENT 0.92594 STRAIN 0.0240 STRESS 1710.2 LIFE 0 to1e8 DAMAGE 10 to1e32 FACTOR OF SAFTY 0.04838 to2.832 BI-INDICATION 0.993 to 0.97666 ALL-STRESS 1710.2 MODE 1 1631.8 MODE 2 2939.1 MODE 3 3033.4 MODE 4 3663.6 MODE 5 4577 MODE 6 5615.1 E-GLASS EPOXY Analysis 10x DISPLACEMENT 0.87737 STRAIN 0.02459 STRESS 1781 LIFE 57.949-1e6 DAMAGE 1000 to 1.7257e7 FACTOR OF SAFTY 0.048 to2.58 BI-INDICATION 0.99 to0.867 ALL-STRESS 1781 MODE 1 1725.5 MODE 2 3086.6 MODE 3 3122.7 MODE 4 3731.6 MODE 5 4772.7 MODE 6 5779.6 Mean stress
- 7. Simulation of Critical Crack Length Propagation… www.ijceronline.com Open Access Journal Page 64 III. CONCLUSION Initially data collection and literature survey was done on critical length on various materials. By analysis in three materials aluminum has high strength and life cycle and damage will be less compared to E- glass epoxy material. In aerospace design epoxy’s are widely used to make outer body’s, these outer bodies caused to damage with small hit or crack initiation so better to use mixture of aluminum and carbon mixture in good qualities. IV. FUTURE SCOPE Epoxy materials are not able to withstand after crossing safe zone (initiation of crack). When we mix the aluminum materials and E-glass epoxy material the material can with stand and life cycle of material can be increased. REFERENCES [1] G. Fajdiga and M. Sraml; Fatigue Crack Initiation and Propagation under Cyclic Contact Loading. [2] Mr. Quinton Row son consultant Structural Integrity, Quest Integrity NZL Ltd., New Zealand Mr. Michael Rock engineering Project Manager, Mighty River Power Ltd., New Zealand; Comparison between ductile tearing analysis and linear elastic fracture mechanics analysis. [3] Donoso, J.R. and Landes; Materials Science Department, Universidad Tecnica Federico Santa Maria Valparaiso, CHILE juan.Donoso@Usm.Cl 2 MABE Department, The University Of Tennessee Knoxville, TN Usalandes@Utk.Edu;An instability analysis for a crack growth situation based on the common format. [4] fracture and fatigue crack growth analysis of rail steels; Journal Of Mechanics Of Materials And Structures [5] M kulkarni1, Ravi prakash2 and A N kumar3; Experimental And Finite Element Analysis Of Fracture Criterion In General Yielding Fracture Mechanics [6] H. Sun, S. Rajendran and D. Q. Song: Finite Element Analysis on Delimitation Fracture Toughness Of Composite Specimens [7] Tipple and G. Thorwald; Using the Failure Assessment Diagram Method with Fatigue Crack Growth To Determine Leak-Before- Rupture.