حسين وسعاد وعبد الجبار Al-Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. A new Cumulative Damage Model Shot Peening Treatment Hussain J. M.Alalkawi Abdul *Department of Electromechanical *** Department of biomedical Engineering *E-mial: **E- ***E-mial: (Received 16 Abstract In this paper, fatigue damage accumulation were studied using many Marsh(CDM), new non-linear model and experimental classical methods, Corton-Dalon (CD)andCorton respectively. However satisfactory predictions were obtain model) for medium carbon steel compared with experimental work are related to their inability to take into accou model shows that a much better and conservative prediction of fatigue life in comp The prediction of the present model gave slightly below the experimental data while the CDM gave overestimate prediction and CD showed strongly underestimates the life of specimens. Keywords: Cumulative fatigue damage, Shot peening, Non 1. Introduction Only a few machine parts are subjected to static loading but many of machine parts are subjected to variable loads. The variable loads have been found by experiment that when a material is subjected to dynamic loads. It fails at a stress below the yield point; such type of failure is known as fatigue. Fatigue may be constant or variable. Constant fatigue loading is defined as fatigue under cyclic loading with constant amplitude and a constant mean stress or load in service the structures or components are subjected to variable amplitude loading, which can be a rather complex load time history [1]. Variable loading or cumulative damage is usually investigated by testing specimens with a definite number of cycles at one stress level, and Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. 57- 64 (2014) Damage Model for Fatigue Life Prediction under Shot Peening Treatment Hussain J. M.Alalkawi* Saad A. Khuder Al Saraf** Abdul-Jabar H. Ali*** Electromechanical Engineering/ University of technology **Ministry of education Engineering /Al-Khawarizmi College of Engineering/ University of Baghdad mial: Alalkawi2012@yahoo.com -mial: alsaraf_saad @yahoo.com mial: Dr.abduljabarha @yahoo.com 16 December 2013; accepted 15 April 2014) mulation were studied using many methods i.e.Corton-Dalon (CD linear model and experimental method. The prediction of fatigue lifetimes based on the two Corton-Dalon-Marsh (CDM), are uneconomic and non respectively. However satisfactory predictions were obtained by applying the proposed non-linear model (present compared with experimental work. Many shortcomings of the two classical related to their inability to take into account the surface treatment effect as shot peening. It is c model shows that a much better and conservative prediction of fatigue life in comparison with CD and CDM methods. prediction of the present model gave slightly below the experimental data while the CDM gave overestimate CD showed strongly underestimates the life of specimens. damage, Shot peening, Non-linear model. Only a few machine parts are subjected to static loading but many of machine parts are variable loads have been found by experiment that when a . It fails at a uch type of failure is known as fatigue. Fatigue may be constant or variable. Constant fatigue loading is defined as fatigue under cyclic loading with constant amplitude and a constant mean stress or load. But in service the structures or components are subjected to variable amplitude loading, which can be a rather complex load time history [1]. Variable loading or cumulative damage is usually investigated by testing specimens with a cles at one stress level, and then to continue the test at other stress level until failure. In these various stress level tests, the stresses may be either in an increasing decreasing order or mixed together [ study a new cumulative fatigue damage model for life prediction will presented involving the effects of loading sequences and the surface treatment. 2. Fatigue Damage Accumulation For long time, researchers have tri the best theory to explain the fatigue damage accumulation behavior. A comprehensive review can be found in [3]. Only a few damage accumulation theories are briefly described below. Al-Khwarizmi Engineering Journal Prediction under ** Khawarizmi College of Engineering/ University of Baghdad CD),Corton-Dalon- e lifetimes based on the two , are uneconomic and non-conservative linear model (present . Many shortcomings of the two classical methods It is clear that the new arison with CD and CDM methods. prediction of the present model gave slightly below the experimental data while the CDM gave overestimate then to continue the test at other stress level until failure. In these various stress level tests, the stresses may be either in an increasing or decreasing order or mixed together [2].In this amage model for life prediction will presented involving the effects and the surface shot peening ccumulation , researchers have tried to find the best theory to explain the fatigue damage accumulation behavior. A comprehensive review can be found in [3]. Only a few damage accumulation theories are briefly described below. mailto:@yahoo.com mailto:@yahoo.com mailto:@yahoo.com Hussain J. M.Alalkawi Al-Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. 57- 64 (2014) 58 Miner [4] first expressed the concept of cumulative fatigue damage in a mathematical formula as, = = 1 … (1) where, is the cumulative fatigue damage and , are the applied cycles and the number of cycles to failure under i-th constant S-N curve stress level respectively. Corton-Dolan theory [5] was based on the modification the S-N diagram. They suggested obtaining the slope of the modified S-N line from the average results of the few repeated two-step block tests expressed as: = + (1 − ) … (2) where is the number of cycles to failure, is the number of cycles to failure at high stress in a constant amplitude test, is the fraction of cycles at , is the ratio of rate of damage, and is an exponent. Corton-Dolan found that was related to the stress amplitude by the empirical equation: =[ ] … (3) where, is the lower stress, and is the inverse slope of S-N curve on a log-log plot. Marsh [6] modified the Corton-Dolan method to include the stress amplitude below the fatigue limit into account. Miller et al [7] showed that damage can be initiated by cycling at stresses below the fatigue limit and so the 0.8 of the fatigue limit stress level was used in conjunction with the Corton-Dolan S-N curve rule. The new method is presented here was named as Corton- Dolan-Marsh theory (CDM). More details about CDM theory can be seen in [7]. Yougming and Sankaran [8] proposed a general methodology for stochastic fatigue damage modeling under variable amplitude loading. This model describes the cumulative fatigue damage in a nonlinear formula which predicts the fatigue life and improves the accuracy of the Miner rule. Two levels fatigue damage model was proposed by Z. Yang et al [9] for low cycle fatigue (LCF) and high cycle fatigue cumulative fatigue damage. The results showed that the predictions of the lives are in good agreement with the experimental results. 3. The Proposed Non-Linear Model Following the work of Perreira et al [10], they suggested the damage due to fatigue under variable amplitude stress such as for low-high and high-low stress level as: = [ ] … (4) where, (α) is a function of the applied load. In the present work, (α) defined as the effect of loading sequences and surface treatment, here the surface treatment is shot peening technique. Equation (4) can be modified to take the form: = [∑ ] … (5) where, ( ) represents the effect of loading sequences and shot peening treatment, ( ) here ( ) defined as: = … (6) where, is the inverse slope of the S-N curve. Equation (6) can be applied from low to high stress level. But when the test program is from high to low stress, equation (6) is changed as following: = … (7) In order to make the prediction safe equation (5) can be divided by the value ( )to become: = [∑ ] … (8) 4. Experimental Work The current work is based on an experimental program which included 72 fatigue specimens, 48 specimens were tested to establish the S-N curves for both dry (without shot peening) and shot peening treatment. The shot peening was done at 10, 20 and 30 minute, 24 specimens were tested under low-high and high-low stress. All specimens were extracted from a medium carbon steel rod with1m long and 10mm in diameter. The chemical composition of the material used is presented in Table (1) while the experimental mechanical properties with the standard values are listed in Table (2). Hussain J. M.Alalkawi Al-Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. 57- 64 (2014) 59 Table 1, Chemical composition of medium carbon steel in wt. %. Element C Si Mn S Fe Experimental 0.4 0.13 1.04 0.002 Blance Table 2, Mechanical properties of medium carbon steel. Mechanical properties Yield strength (MPa) Ultimate strength (MPa) Elastic modules (GPa) HV Experimental 295 585 207 184 5. Fatigue Test Procedure The specimens were prepared according to DIN 50113.The specimens are manufactured using programmable CNC lathing machine. Figure (1) shows the fatigue test specimens and its configuration. All fatigue tests were carried out in the laboratories of electromechanical engineering department, University of Technology using fatigue testing machine type PUNN rotating bending Figure (2). The experiments were conducted at room temperature and at stress ratio R=-1(minimum stress to maximum stress in periodic cycle), while the shot peening device with its properties can be seen in Ref. [12]. Fig. 1. Specimen geometry and dimensions for fatigue test (all dimensions in mm). 0.5×45° 30 30 80 Ø 10 Ǿ 6. 74 R=30 20 Hussain J. M.Alalkawi Al-Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. Fig. 2. PUNN rotary fatigue bending machine 6. Results and Discussion Constant stress amplitude with stress ratio (R=-1) at room temperature tests were conducted in order to use the parameter ( , inverse slope of S-N curve) for driving the present model. The final results can be summarized in Table ( Table 3, Basic S-N fatigue results at room temperature (RT) Description Dry (without shot peening) with shot peening (SPT) 10 min. with shot peening (SPT) 20 min. with shot peening (SPT) 30 min. 6.1. Variable Amplitude Results (Cumulative Fatigue Damage) The cumulative fatigue damage tests have been conducted for two-steps program low Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. 60 PUNN rotary fatigue bending machine. stress ratio were conducted , inverse slope of N curve) for driving the present model. The final results can be summarized in Table (3) equation of power law regression is given (fatigue life formula). = where, ( ) is the applied stress, and ( fitting parameters. The regression represent of the fatigue trends. room temperature (RT). b a -0.235 5623 -0.296 7650 -0.252 9120 -0.272 10690 Variable Amplitude Results The cumulative fatigue damage tests have steps program low-high and high-low stress for the conditions mentioned in Table (4). The experimental cumulative fatigue damage results are listed in Table (4 Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. 57- 64 (2014) equation of power law regression is given by … (9) ) is the applied stress, and (a),(b) are the regression constants nditions mentioned cumulative fatigue results are listed in Table (4). Hussain J. M.Alalkawi Al-Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. 57- 64 (2014) 61 Table 4, Experimental cumulative fatigue damage results. 6.2. Comparison Between Fatigue Life Prediction Methods Comparisons between the four methods of fatigue life prediction can now be done. The predictions of fatigue lifetime using Corton-Dolan (CD) and Corton-Dolan-Marsh (CDM) methods with the experimental and the new model results are illustrate in Table (5). Table 5, Comparison between fatigue lives prediction between four methods. The CD and CDM have been shown not to be satisfactory for predicting life in a two-step loading due to their inability to take into account the effect of shot peening which decelerate the short cracks. Figures (3 and 4) show the four methods in comparison for predicting the fatigue life with the experimental results. Nf(Cycles) Average Amplitude stress (MPa) Loading program Description 487000 130467 275-450 450-270 Low-High High-Low dry (without shot peening) 954000 195000 275-450 450-270 Low-High High-Low with shot peening (SPT) 10 min. 1623330 353210 275-450 450-270 Low-High High-Low with shot peening (SPT) 20 min. 1077261 188200 275-450 450-270 Low-High High-Low with shot peening (SPT) 30 min. Nf Cycles Model Nf Cycles experimental Nf Cycles CDM Nf Cycles CD Loading program SPT Min. 469913 124605 487000 130467 1388436 494209 32103 85837 Low-High High-Low dry 849175 183003 954000 195000 2312581 670972 45299 68259 Low-High High-Low SPT10 1288140 238894 1623330 353210 3538197 1402019 50813 70423 Low-High High-Low SPT20 805395 159619 1077261 188200 2635364 460404 42319 57176 Low-High High-Low SPT30 Hussain J. M.Alalkawi Al-Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. 57- 64 (2014) 62 Fig. 3. shows the Low-High cumulative fatigue life prediction for four methods. Fig. 4. shows the High-Low cumulative fatigue life prediction for four methods. It is clear that the new model shows that a much better and conservative prediction of fatigue life in comparison with CD and CDM methods. The prediction of the present model gave slightly below the experimental data while the CDM gave overestimate prediction and CD showed strongly underestimates the life of specimens. 7. Conclusions 1. For this particular loading and metal used, the proposed non-linear model (present model) seems to be a proper choice for cumulative fatigue damage life prediction. 2. The CDM predictions showed that non- conservative prediction (overestimate the life) based on the experimental results. 0 500000 1000000 1500000 2000000 2500000 3000000 3500000 4000000 dry SPT10 SPT20 SPT30 CDM CD Experimantal Model 0 200000 400000 600000 800000 1000000 1200000 1400000 1600000 dry SPT10 SPT20 SPT30 CDM CD Experimantal Model Hussain J. M.Alalkawi Al-Khwarizmi Engineering Journal, Vol. 10, No. 2, P.P. 57- 64 (2014) 63 3. The CD method gave uneconomic predictions(strongly underestimates the life) compared to the experimental results. 8. References [1] N. E. Frost, K. J. Marsh and L. P. Pook “Metal Fatigue” Clarendon Press, Oxford (1974). [2] Alakawi H. J. M. “Cumulative fatigue damage under varying stress range conditions” phD. Thesis, university of Sheffield uk (1986). [3] Fatemi, A. Yang L. “Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogenous materials” Int. J. Fatigue, 20-9-34 (1998). [4] Miner M. A. “cumulative fatigue damage” J. of applied Mechanics, 67, A159-A164 (1945). [5] Corten H. T. and Dolon T. J. “Cumulative fatigue damage”Proc. Int. Conf. Fatigue of metals, London, Instn. Mech. Eng., pp234- 246 (1956). [6] Marsh K. J. “Cumulative fatigue damage under symmetrical saw tooth-loading program” Mech. Eng. Science, 7, pp. 138- 151(1965). [7] Miller K. J., Mohamed H. j. and de los Rios. “Fatigue damage accumulation above and below the fatigue limit” European Group on fracture publication No. 1, EGFI, Instn.Mech. Eng. London (1986). [8] Yongming Liu, SankaranMahadevan “Stochstic fatigue damage modeling under variable amplitude loading” International Journal of fatigue 39, 1144-1169 (2007). [9] Zhi Yong Huang, Daniele Wagner, Claude Bathias, Jean Louis Chaboche “cumulative fatigue damage in low cycle fatigue and high cycle fatigue for low carbon-manganese steel” International Journal of fatigue 33, 115-121 (2011). [10] H. F. S. G. Perreira, A. M. P. Jesus, A. S. Ribeiro, A. A. Fetenades “Fatigue damage behavior of structural components under variable amplitude loading” Mechanica Experimental, Vol. 17, 75-85 (2009). [11] H. J. Alalkawi, Kiffaya A. Al saffar, Mohammed J. K. “fatigue-Creep interaction of copper alloy C35600 under variable temperature” Implementation of postgraduates researchers to serve the society 7-8May (2012) Al mustansiriya university. [12] H. J. Alalkawi, R. A. Mairb, N. A. Fatin “Shot peening treatment as a barrier to fatigue crack propagation in pure shear for medium carbon steel” journal of Al-Taqani (2010). )2014( 57- 64، صفحة 2، العدد10دجلة الخوارزمي الھندسیة المجلم حسین جاسم 64 للتنبؤ بعمر الكالل تحت تأثیر معالجة السطوح بالنقر المستمر أتموذج الضرر التراكمي الجدید ***عبد الجبار حسین علي** سعد عباس خضر* حسین جاسم العلكاوي الجامعة التكنولوجیة/ قسم ھندسة الكھرومیكانیك * وزارة التربیة/ مدیریة التعلیم المھني ** يوارزمكلیة الھندسة الخ/ الحیاتي قسم ھندسة الطب *** Alalkawi2012@yahoo.com : البرید االلكتروني* yahoo.com alsaraf_saad@ :البرید االلكتروني** yahoo.com Dr.abduljabarha@ :البرید االلكتروني*** الخالصة دایلن - طرق ؛ كورتن عدةبأستخدام )medium carbon steel ( ل لسبیكة الصلب المتوسط الكاربوفي ھذا البحث تم دراسة حساب تراكم ضرر الكال )CD ( ، مارش –دایلن –كورتن (CDM) دایلن - یستند تنبأ عمر الكالل على اسلوبین تقلدیین ھما كورتن. بضمنھا االنموذج المقترح مقارنة بالنتائج العملیة (Corton-Dalon) مارش - دایلن - و كورتن (Corton-Dalon-Marsh)في حین . وھي غیر أقتصادیة وغیر دقیقة مقارنة مع النتائج العملیة على التوالي یرتبط العدید من أوجة القصور . الكالل للسبیكة التي استخدمت في البحث بأستخدام االنموذج الالخطي المقترح مناسبا مقارنة بالنتائج العملیةكان التنبأ بعمر االنموذج ).shot peening( نقر المستمرفي االسالیب الكالسیكیة التقلیدیة المشار الیھا بعدم قدرتھا على أن تأخذ في االعتبار تأثیر المعالجة السطحیة مثل ال اعطى نتائج اعلى بكثیر من النتائج العملیة وان اسلوب CDMمن النتائج العملیة في حین ان اسلوب بقلیل المقترح لتنبأ بعمر الكالل اعطى نتائج تقریبا اقل CD اعطى نتائج اقل بكثیر من النتائج العملیة. mailto:@yahoo.com mailto:@yahoo.com mailto:@yahoo.com