NONLINEAR CONSTANT LIFE MODEL FOR FATIGUE LIFE PREDICTION OF - PDF document

18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS NONLINEAR CONSTANT LIFE MODEL FOR FATIGUE LIFE PREDICTION OF COMPOSITE MATERIALS T. Park 1 , M. Kim 1 , B. Jang 1 , J. Lee 2 , J. Park 3 * 1 Graduate School, Korea Aerospace University, Koyang, Republic of Korea, 2 Smart UAV Development, Korea Aerospace Research Institute, Daejeon, Republic of Korea, 3 School of Aerospace and Mechanical Engineering, Korea Aerospace University, Koyang, Republic of Korea * Corresponding author (jungsun@kau.ac.kr) Keywords : Composites, Life prediction, S-N curves, Constant life diagram life is possible with increasing number of S-N 1 Introduction Composite materials are widely used to aircraft and curves. But it cannot properly describe for fatigue spacecraft due to its light-weight, yet excellent behavior with varying R -ratio when fewer S-N mechanical properties compared to metal by using curves available due to its linear characteristics. its directional characteristics. Many studies have Kawai[7,8] proposed a nonlinear CLD that can be been done for fatigue failure of composite material derived by using only one “critical” S-N curve. The because fatigue is one of the main causes of failure. critical R -ratio is equal to the ratio of the UCS over For estimating the fatigue life, the critical points are UTS of the examined material. The main drawback the S-N type selection, statistical interpretation of of this model is the need for experimental data for fatigue data, selection of the appropriate constant this specific S-N curve. Therefore, it cannot be life diagram formulation, fatigue failure criterion, applied to existing fatigue databases. However, the and the damage summation rule [1,2]. Among these minimum amount of data required is an advantage of critical points, we focused on the effect of CLD the methodology. In this study, a nonlinear constant formulation on life prediction. life diagram formulation is proposed and the The classic linear Goodman diagram[3] is the most influence of the constant life diagram formulation on widely used CLD, because of its simplicity. But it is the prediction of the fatigue life was examined. The not suitable for composite materials because of its proposed model needs three or more S-N curves and damage mechanisms under tension and compression requires nonlinear regression process. With a small is different. Therefore straight lines connecting the number of available S-N curves, proposed CLD UTS and UCS with points of the R   line for model can describe fatigue behavior more properly 1 different numbers of cycles are not capable to with varying R -ratio compared to piecewise linear describe the fatigue behavior of composite materials. model which is currently the most accurate CLD. Several different models have been presented in the The most commonly used CLD formulations are literature to properly describe characteristics of evaluated according to its accuracy of estimation for composite materials. Starting from the basic idea of unknown S-N curves. Based on the results, Goodman diagram and the nonlinear Gerber recommendations concerning the applicability, equation, different modifications were proposed. advantages and disadvantages of each of the Based on the linear interpolation between different examined CLD formulations are discussed. S-N curves in a modified Goodman diagram concept[4-6], analytical expressions of any desired 2 Theories of CLD model S-N curve so called piecewise linear CLD is Constant life diagram was created to consider the developed by Philippidis et al [2]. Comparison of effect of the mean stress and material anisotropy on CLDs by predicting ability of new S-N curve shows the fatigue life of the composite material. CLD acts that piecewise linear CLD is the most accurate of the as a master diagram and represents constant fatigue compared formulations when more than three S-N life behavior for entire range of loading type (comp- curves available. More accurate estimation of fatigue

ression-compression, tension-compression, and tens- where,  and  are the stress amplitudes ' a ' a TT ,1 ion-tension loading). CLD makes it possible to corresponding to R and , respectively and ' R 1 TT estimate S-N curve for specific loading patterns for       (1 ) / (1 ) , and ' (1 ') / (1 ') . r R R r R R which no experimental data exist. The main i i i 2. If R is located between any of two known R -  parameters of CLD are the mean stress, , the m ratios, R i and R i+1 , alternating stress,  , and the R -ratio, which defined   ( ' ) a r r ,  1   (4) as the minimum stress over the maximum stress. ' a i i  a ,  a i   ( ') ( ' ) r r r r  1  i  i , 1 2.1 Linear CLD a i 3. If R ’ is in the C-C region of the CLD, and The linear CLD model is based on a single S-N curve that should be experimentally derived under between UCS and first known R-ratio in the R   ). Constant life lines fully reversed loading( compression region, , 1 R 1 CC are created by connecting constant life data points UCS   (5) ' and static strength. Unknown S-N curves are simply a UCS   ' r r CC calculated by linear interpolation. This CLD model  1 ,1 a CC constitutes a modification of the Goodman line[3]. where,  and  are the stress amplitudes ' a ' a CC ,1 The general formulae of the model are: corresponding to R and , respectively. ' R        (1) 0 (1 ( / )), 0 1 CC UTS For a a m m        (2) 2.3 Kawai’s CLD [7,8] 0 (1 ( / )), 0 UCS For a a m m where,  is the cyclic stress amplitude for a given Kawai and his coworkers developed an asymmetric 0 a constant value of life N under fatigue loading. constant life diagram, designated the anisomorphic constant fatigue life (CFL) diagram in [7]. Main 2.2 Piecewise linear CLD [2] feature of this formulation is that it can be The piecewise linear CLD is derived by linear constructed by using only one experimentally interpolation between known S-N curves in the derived S-N curve, which is called critical S-N curve.    plane. A limited number of experimentally ( ) The R -ratio of this S-N curve is defined as the ratio m a of the UCS over UTS of the material. The determined S-N curves along with the ultimate formulation is based on three main assumptions: 1. tensile and compressive stresses of the materials are The stress amplitude for a given constant value of required for this CLD model. Typically, S-N curves fatigue life is greatest at the critical stress ratio. 2. representing the entire range of possible loading are The shape of the CFL curves changes progressively used for piecewise linear CLDs, normally at from a straight line to a parabola with increasing R  R   for tens- 0.1 for tension-tension loading, 1 fatigue life. 3. The diagram is bounded by the static ion-compression loading, and R  for compress- 10 failure envelope that consists of two straight lines ion-compression loading patterns. Constant life lines connecting the peak point on the critical straight line are constructed by connecting the same fatigue life with the UTS and UCS, respectively. The CFL cycle data points on each of the S-N curves. By formulation depends on the position of the mean linear interpolation between known values of fatigue stress, σ m , in the domain [ σ C, σ T ] as follows. and strength data, unknown S-N curves are      estimated. Following analytical expressions for the   (2 )      ( )  ,  m m UTS description of each region of the piecewise linear        m m  UTS    (6) m a a CLD were developed in [2].          (2 )      a ( ) , m m  1. If R ’ is in the T-T sector of the CLD, and UCS     m m  UCS m between UTS and the first known R -ratio in the where,   and   represent the alternating and tension region, , a m R mean stress components of the fatigue stress for a 1 TT UTS given constant value of life N under fatigue loading   (3) ' a UTS   at the critical stress ratio,   The ' / . r r UCS UTS  1 TT ,1 a TT