International Conference on Mechanical, Electronics and Mechatronics Engineering (ICMEME'2012) March 17-18, 2012 BangkokFatigue Crack Initiation and Propagation Life Prediction of Materials Y. S. Upadhyaya and B. K. Sridhara Abstract— Strain controlled fatigue life of EN 19 steel and 6082T6 aluminum alloy have been predicted considering both crack initiation and crack propagation phases. Continuum Damage Mechanics (CDM) approach models the crack initiation life with a damage value and damage beyond the crack initiation phase is predicted by Fracture Mechanics in terms of crack size. Fatigue life is predicted for a smooth (un-notched) specimen in the strain amplitude range of 0.3 % to 0.7 %, in room temperature at stress ratio of -1. The inputs required for both the models have been determined by conducting monotonic, cyclic, fracture toughness and fatigue crack growth tests. Predicted life is also compared by conducting strain controlled fatigue tests and predicted life compares well with the experimental life. The results show that by using monotonic, cyclic and fracture parameters of a material available in literature and by conducting Multiple Step Test on one fatigue specimen, it is possible to determine strain controlled crack initiation and crack propagation life of metals and alloys. Keywords— Continuum damage mechanics, fatigue, fracture mechanics, life prediction. I. INTRODUCTION HE components used in aircraft, space and automobile applications are designed based on fatigue consideration. Time varying cyclic loads result in failure of components at stress values below the yield or ultimate strength of the material. This phenomenon is called fatigue and fatigue failure of components takes place by the initiation and propagation of a crack until it becomes unstable and then propagates to sudden failure. The total fatigue life is the sum of crack initiation life and crack propagation life. Fatigue life prediction has become important because of complex nature of fatigue as it is influenced by several factors, statistical nature of fatigue phenomena and time consuming fatigue tests. Though a lot of fatigue models have been developed and used to solve fatigue problems, the range of validity of these models is not well defined. No method would predict the fatigue life with the damage value by separating crack initiation and propagation phases. The methods used to predict crack initiation life are mainly empirical [1] and they fail to define the damage caused to the material. Y. S. Upadhyaya is working as Assistant Professor with Department of Mechanical and Manufacturing Engineering, Manipal Institute of Technology, Manipal University, Manipal - 576 104, India. (phone: +91 0820 2925463; fax: +91 0820 2571071; e-mail: [email protected]). Dr. B. K. Sridhara is working as Professor with Department of Mechanical Engineering, The National Institute of Engineering, Mysore - 570 008, India. (e-mail: [email protected]). T Stress or strain based approaches followed do not specify the damage caused to the material, as they are mainly curve fitting methods. The Fracture mechanics approaches are suited for the situations in which it is not necessary to know state of stress or damage in the vicinity of crack tip. Loading configuration issues and use of experimental fracture mechanics data to components may not be appropriate if situations such as complex crack size and shape, pronounced plasticity or multiple cracking, are involved. These limitations of fracture mechanics motivated the development of micromechanics models termed as local approaches based on Continuum Damage Mechanics (CDM). The local approaches are based on application of micromechanics models of fracture in which stress/strain and damage at the crack tip are related to the critical conditions required for fracture. These models are calibrated through material specific parameters. Once these parameters are derived for particular material, they can be assumed to be independent of geometry and loading mode and may be used to the assessment of a component fabricated from the same material. Ductile fracture in metals involves considerable plastic damage via, nucleation, growth and coalescence of microvoids. The phenomenon of initiation and growth of cavities and microcracks by large deformations in metals is called ductile plastic damage. This has been extensively studied by means of micromechanics and continuum damage mechanics models [2, 3, 4]. All models mentioned above are a good representation of physical mechanism at the microscale level, but difficulties arise when these are to be included in large scale structures to predict ductile failures. This difficulty has been overcome by developing model incorporating damage variable with the concept of effective stress. This stress, written as the mean density of forces acting on the elementary surface that effectively resists, has been introduced by Kachanov [5] to model creep rupture. The CDM approach has been developed further for dissipation and low cycle fatigue in metals [6], for coupling between creep and damage [7] and for creep fatigue interaction [8]. Later the thermodynamics of irreversible process provided the necessary scientific basis to justify CDM as a theory [9]. The degradation in mechanical properties due to damage is an irreversible phenomenon, which takes into account the effect of damage on the mechanical properties of materials and the influence of external conditions on subsequent development of microvoids. This concept was further developed and applied by Lemaitre [10], Simo and Ju [11] and Chaboche 13 The plastic strain corresponding to fracture ductility ε f . but is the point at which the damage causing process becomes localized and leads to the growth of a dominant defect. Chandrakanth and Pandey [13] developed an isotropic ductile plastic damage model in the framework of internal variable theory of thermodynamics. A nonlinear CDM model developed by Jing Jian Ping et al. damage is isotropic and ductile in nature. Damage is considered as isotropic in this study. ductile damage and creep damage. term damage refers to surface density of cracks and cavities in a section (CDM definition) at lower strain amplitudes and crack size (Fracture Mechanics definition) at higher strain amplitudes.International Conference on Mechanical. Therefore in CDM. it is possible to predict crack initiation and crack propagation life in fatigue loading. damage corresponding to the onset of rupture is termed as critical damage and in fatigue or creep it is associated with initiation of a macroscopic crack. shows the application of CDM model to a component. Ẽ = E(1-D) (2) Equation (2) helps to estimate the state of damage in a deformable material by experimentally determining its reduced modulus of elasticity. a dimensionless number between zero and one. 20] also shows the application of CDM at component level. other research work [19. C 2 are functions of monotonic stress-strain parameters. [16] developed a thermodynamics based CDM model to predict the high cycle fatigue life. Abilio Jesus [15] formulated a fatigue model in the framework of CDM based on an explicit definition of fatigue damage. Also wide range of CDM models to predict life in case of low cycle fatigue.85 [23]. on an elemental cross-sectional plane is quantified by the surface density of cracks and cavities at that section [10]. at load levels . In slow ductile deformation. If damage can be considered the same regardless of the orientation of the cross section on which it is measured. D=0 for undamaged material and D=1 for fully broken material in two parts. Both E and Ẽ are related by applying eq . Here. as mentioned in eq.damage variable If E is the modulus of elasticity of undamaged material . This critical damage termed as D c. D c is an intrinsic material property [24] and it helps to predict the failure in a complex loading situation by using the value of D c obtained from a simple static tension test carried out on the same material and at same temperature. In this approach. According to this model. gives the critical damage for the material as D= 1− C2 ε + C1 1+ n p (3) where ε p is plastic strain. Therefore. failure is not necessarily fracture. multiaxial loading. applied to effective stress-actual strain relationship. The basic assumption made in the Lemaitre’s model as. Using the effective stress concept. Electronics and Mechatronics Engineering (ICMEME'2012) March 17-18. Lemaitre’s model [10] is one of the models based on the phenomenological approach. B. The model establishes a relation among damage. In the context of CDM. generally vary in the range between 0. damage initiates only after the accumulation of threshold plastic strain. developed an isotropic damage growth model under uniaxial (monotonic) loading by using the constitutive law described by Ramberg-Osgood model. Isotropic damage model for uniaxial loading Baidurya and Bruce [17]. specimen/component. Similarly. Xiao et al.effective stress considering the defect in the section D . CDM based fatigue damage model for crack initiation Fatigue failure occurs. According to the phenomena of ductile damage. LIFE PREDICTION MODELS In CDM. have been developed. A good agreement between the theoretical log S . high cycle fatigue. [18] to assess the low cycle fatigue life of 200 MW steam turbine rotor under cold start and sliding parameter stop. Marcilio et al. the damage. creep-fatigue interaction. a general statement is made as. after number of cycles. (1) to the elastic strain tensor by assuming that the Poisson’s ratio is not affected by damage [21]. [22] have developed a numerical simulation method. These models are based on the concepts of Kachanov [5] and they account for different loading conditions. by combining both CDM and fracture mechanics approach. variable amplitude loading. From these literatures it is clear that CDM approach has the main advantage of transferability of data from specimen level to component level. Considering the experimental difficulties to determine the reduced modulus of elasticity.log N curve by using this model and experimental one is obtained. Yingchun Xiao [14] developed an isotropic CDM framework which can reasonably show the interaction mechanism of brittle damage.nominal stress σ ̃ . (2). 2012 Bangkok [12]. Thermodynamics based CDM model developed by Baidurya and Bruce [17] predicts crack initiation life for strain controlled fatigue loading.15 and 0. plastic strain at threshold and the critical damage corresponding to the void growth and void coalescence respectively are set as criterion to describe the material degradation. According to the model. the 14 nominal stress is related to effective stress through the damage variable in the material as σ ̃ = σ/(1-D) (1) σ . n is strain hardening exponent and C 1 . D. failure occurs when the damage variable equals the critical damage D c ≤ 1. plastic strain and two constants which could be derived using monotonic stressstrain parameters. plastic strain is mainly responsible for damage growth. II. A parallel approach to the micromechanical approach based on CDM is the phenomenological approach. then Ẽ is considered as modulus of elasticity of damaged material . and is quantified by one single scalar variable. then damage is isotropic. damage evolution is defined in terms of a single variable. A. 6 strength (σ f ) MPa coefficient.International Conference on Mechanical. additional damage is introduced in the material.12 0. MATERIALS AND METHODOLOGY The objective of the present study is to predict strain controlled fatigue life of materials by considering a ferrous and a nonferrous material. Crack initiation occurs when the critical value of damage is reached. n TABLE IV MONOTONIC PROPERTIES OF 6082-T6 ALUMINUM ALLOY Mean Mean Properties Properties value value Ultimate tensile True fracture 349. No. is maintained during the test. IV. These material properties have been determined for EN 19 steel and 6082-T6 aluminum alloy by conducting monotonic. 26]. cyclic.744 strength (S u ) MPa ductility (ε f ) 0. C. developed model to predict the number of cycles for crack initiation in case of strain controlled loading. TABLE III MONOTONIC PROPERTIES OF EN 19 STEEL Mean Properties Mean Properties value value Ultimate tensile True fracture 749. in the positive stress region causes damage to increase [25. various material properties are required. the predicted results have been compared with experimental results by conducting strain controlled fatigue tests. S e . N i is the cycles to macroscopic crack initiation (localization). cyclic. but above the endurance limit. The monotonic properties have been determined as mean of results of 8 specimens and are shown in Table III and Table IV for both the materials. EN 19 steel (a 1% typical chromium molybdenum steel with higher molybdenum) and 6082-T6 (solution heat treated. All these different types of tests have been conducted on a ±50 kN axial type srvohydraulic testing machine as per the respective ASTM standards and details of each test is mentioned below in brief. 2012 Bangkok below the static monotonic failure stress. artificially aged and alloyed with manganese.065 0.04 The predicted fatigue life correspond to smooth specimen subjected to strain controlled fatigue loading in room temperature at stress ratio of -1.4 strength (σ f ) MPa coefficient. on smooth specimen at room temperature. Fracture Mechanics based fatigue crack growth model Crack propagation life is estimated using Paris equation [27] and for this initial crack length. is approximately estimated [27] as a i =(∆K th /2S e )2/π (4) where S e is endurance strength of material and ∆K th is the long crack threshold stress intensity. silicon) aluminum alloy are considered in the present study. unloading portion of a hysteresis loop and compressive stresses are assumed as not to contribute to damage. III. properties reported by researchers are different.6 0.97 % by weight 1. MATERIALS CHARACTERIZATION In order to use CDM and Fracture Mechanics models for fatigue life predictions. of cycles. were prepared as per ASTM standard E8-04 [28].23 TABLE II CHEMICAL COMPOSITION OF 6082-T6 ALUMINUM ALLOY Constituents Si Cu Fe Mn Mg Pb 15 . and the damage at the end of one cycle acts as the initial damage for the damage increment in the next cycle. Final crack length corresponds to fracture toughness of the material.2 11.196 0. K (MPa) Modulus of Monotonic strain 185 0.027 0. Monotonic test Specimen of 6.35 mm of gauge diameter and having threaded ends for gripping.35 strength (S y ) MP 25 mm gauge True fracture Monotonic strength 477.411 0.2 % offset yield % elongation on 329 10. fracture toughness and fatigue crack growth tests on both the materials. With each cycle. The literature shows that.2 % offset yield % elongation on 591.77 0. Finally. Baidurya and Bruce [17]. not much work has been done on the strain controlled fatigue life prediction with the damage value for EN 19 steel and 6082-T6 aluminum alloy.022 0. The literature shows that for the same nominal grade of a material. 6082 is typically used in trusses.696 strength (S u ) MPa ductility (ε f ) 0. Extensometer of 25 mm is used and a stroke rate of 2 mm/ min. EN 19 steel is used for gears and high strength shafts and its chemical composition is shown in Table I. A total of 8 specimens have been tested to get consistency in the monotonic properties. Specimens of EN 19 steel have been prepared by using a single rod of 80 mm diameter and 6082-T6 aluminum alloy specimens are prepared from the single 150 x 30 mm flat bar. a i .3 0.746 0. Therefore. bridges and transport applications and its chemical composition is shown in Table II. An important parameter which decides the crack initiation criteria is critical damage D c and is obtained by CDM based uniaxial loading model.1651 elasticity (E) GPa hardening exponent. Electronics and Mechatronics Engineering (ICMEME'2012) March 17-18. In any given cycle.3 1596. in this study. Consequently. fracture toughness and fatigue crack growth test. A. apart from monotonic properties and cyclic properties of the material.2 430.712 0. a dummy test was conducted and the results obtained were correct. Initially for a known material. K (MPa) Mo 0. Therefore.97 strength (S y ) MP 25 mm gauge True fracture Monotonic strength 1072. all inputs required for the model have been determined by conducting monotonic. TABLE I CHEMICAL COMPOSITION OF EN 19 STEEL Constituents C Si Mn S Cr % by weight 0. Using Ramberg-Osgood model for the hysteresis loop and the principle of strain equivalence. The model demands input in terms of parameters of hysteresis curve. only the reloading section above the endurance limit. 25 mm.2% with step increment of 0. the constants C and m have been modified for R = -1. Averaging these values. ΔK th = 9. Cyclic test The cyclic stress-strain response of a material is characterized by the cyclic stress-strain curve (CSSC). As the experimental and assumed value of K IC are close.37. The stress-strain curve have been obtained by MST for both the materials.1 and Fig. the design of C(T) specimen in terms of thickness is valid. B (5) > 2. though the FCG test is conducted using C(T) specimen at R=0. In MST procedure single specimen is subjected to multiple steps of fully reversed axial strain cycles. Electronics and Mechatronics Engineering (ICMEME'2012) March 17-18. Using the experimental value of K IC and eq. The literature shows that majority of researchers. 2012 Bangkok Modulus of elasticity (E) GPa Monotonic strain hardening exponent. It is also observed that. Crack initiation life corresponds to an approximate crack size obtained using eq. 20 16 . FCG test is conducted using C(T) specimen having a thickness of 6. (4) and this size is the initial crack size for crack growth model.1 MPa √m for 6082-T6 aluminum alloy. correspond to thickness of 12. The predicted crack initiation and crack propagation life are as shown in Fig.7 MPa and cyclic strain hardening exponent n’ = 0. using Walker equation [27]. Fracture toughness values have been obtained for all the specimens.2 Hz. Fracture toughness (K IC ) test Fracture toughness is a material property and is influenced by material thickness. A comparison of results obtained by different tests [29] shows that MST procedure is recommended as it uses only one specimen and also gives good result. CSSC is defined as the dependence of the saturation stress amplitude on saturation plastic strain amplitude. the plane strain fracture toughness value. Using experimental curve of da/dN vs ΔK and Walker equation. MST procedure is followed to determine CSSC at 0.1% using one fatigue specimen.5(K IC /S y )2 and 25 mm specimens. Initial precracking is done by fatigue loading and fracture toughness value is obtained by tensile loading. as per ASTM standard E647-00 [33]. in the strain amplitude range from 0. D. As all fatigue tests are carried out at R = -1.3. FCG test be also conducted at R = -1.5. Crack propagation life is sensitive to initial crack size. CSSC could be determined from Companion Specimen Test (CST) or Multiple Step test (MST) or Incremental Step Test (IST). Therefore here.8 MPa √m for EN 19 steel and K IC = 21. to model the crack growth. being applied one after other.1543 (for EN 19 steel) and cyclic strength coefficient K’ = 527.37. 20 & 25 mm are considered using eq (5) for both materials.35 mm gauge diameter and with threaded ends for gripping as per ASTM standard E606-92 [30]. m=3. 2. until saturation is achieved at each step. plane strain fracture toughness of the material is determined as it is independent of material thickness.54 MPa √m (for 6082-T6 aluminum alloy) at R= -1. ΔK th = 13.0525 B. Cyclic properties of a material presented as cyclic strength coefficient K’ and cyclic strain hardening exponent n’ are obtained by determining cyclic stress strain curve.44 (for 6082-T6 aluminum alloy). conduct FCG test using C(T) specimens. recommended K IC = 44. Therefore. FATIGUE LIFE PREDICTION AND VALIDATION Using isotropic damage model of uniaxial loading as mentioned in eq. and the notch is obtained by wire cut EDM method. C. V. cyclic properties are determined as cyclic strength coefficient K’ = 1512.International Conference on Mechanical. calculated value for C= 3. Fatigue crack growth test Fatigue crack growth (FCG) test is required to determine the constants C. Fracture toughness test is conducted on Compact Tension C(T) specimens as per ASTM standard E399-90 [31]. The C(T) specimen is not recommended for tension compression testing because of uncertainties introduced into the loading experienced at the crack tip [33]. (5). Fatigue specimens required for MST and fatigue test have been designed for 6. each step with different strain amplitude.9 0. m.1% to 1. by integrating between the initial and final crack size.54 (for EN 19 steel) and D c =0. used in the Paris equation. Assuming K IC = 50 MPa√m for steel and K IC = 25 MPa √m for aluminum [32]. Here.84 x10-10 . Crack propagation life is determined using Paris equation. Crack initiation life is obtained using CDM based fatigue model and input to the model have been provided by cyclic test result and the parameters of stabilized hysteresis curve. critical damage D c is obtained at ε p = ε f and its value is D c =0. as it best models crack growth in an opening mode. m=3. C(T) specimen thickness of 12.5.5 MPa and cyclic strain hardening exponent n’ = 0. All specimens have been prepared as per ASTM standard E39990 [31]. These test methods are different because of strain cycling of test specimens and the number of test specimens required. The crack in fatigue loading initiates at D = D c . The da/dN vs ΔK curve obtained from FCG test on EN 19 steel and 6082-T6 aluminum alloy at R=0.23 MPa √m (for EN 19 steel) and C= 4. n 73. (4) and monotonic properties. crack initiation life is sensitive to each parameter of the stabilized hysteresis curve.37x10-10 .1124 (for 6082-T6 aluminum alloy). By plotting stabilized stress vs plastic strain amplitude in a log-log plot.3. pp. cyclic and fracture parameters of a material are available in literature for a material. Introduction to Continuum Damage Mechanics. Springer-Verlag. and Norman Jones. of Engg. 581-588. and J. “Continuum damage mechanics . and Xia Song Bo. M. A. Meng Guang. vol. Marcilio Alves. and C. pp. 1757-1779.2 Hz frequency and at stress ratio of -1.7. 1977. of Engg. Mech. 2004. vol. M. 55. of Solids & Struct. 35. The predicted total life agrees with the test values within experimental error. and struct.” Theoretical and Appl. Li. Jing Jian Ping. of Solids and Struct. 503-508. Mech. J. and Des. Mater. 363-371. J. Bangalore. Mech. 1999. of Mech. Gurson. J. Krajcinovie. 703-712. India. Vessel. Bathias. pp. Gao. 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