J Fail. Anal. and Preven. https://doi.org/10.1007/s11668-020-00840-x TECHNICAL ARTICLE—PEER-REVIEWED Delamination Detection in Mono Composite Leaf Spring by Modal Curvature and Flexibility Approaches N. I. Jamadar . S. B. Kivade . Rakesh Roshan . Himanshu Dhande Submitted: 13 December 2019 / in revised form: 11 January 2020 Ó ASM International 2020 Abstract The premature failure analysis of laminated composite structures through damage inspections at initial level has gained considerable importance in recent years. Delamination is one of the major failure mechanisms which occur due to low inter-laminar fracture toughness of the matrix in composite structures. Detection of delamination is crucial to ensure safety and reliable use of composites. In the paper, the modal curvature and flexibility methods have been applied for delamination detection in composite leaf spring through analytical and finite element approaches. First, finite element models of healthy and delaminated leaf spring are formulated to evaluate the Eigen value and Eigen vectors. Next, the absolute curvature difference and change in flexibility in both springs are determined after mass normalization. The presence, location and severity of delamination in a spring are found through change in absolute modal curvature and difference in local flexibilities. The modal curvature method precisely identifies the delamination location and its severity than the modal flexibility method. Keywords Failure analysis  Modal flexibility  Modal curvature  Composite leaf spring  Analytical  Healthy spring  Delaminated spring List of symbols Me Me Ke Ke le K K M M U ½F hx ½F dx Uxi N. I. Jamadar (&)  R. Roshan  H. Dhande Dr. D. Y. Patil Institute of Technology, Pimpri, Pune, Maharashtra, India e-mail: jamadar94@gmail.com S. B. Kivade Basavakalyan Engineering College, Basavakalyan, Bidar, Karnataka, India D½F  MðxÞ M  ðxÞ Elemental mass of healthy beam Elemental mass of delaminated beam Elemental stiffness of healthy beam Elemental stiffness of delaminated beam Elemental length of beam Assembled stiffness matrix of healthy beam Assembled stiffness matrix of delaminated beam Assembled mass matrix of healthy beam Assembled mass matrix of delaminated beam Eigen vector Flexibility matrix of healthy beam at distance x Flexibility matrix of delaminated beam at distance x Mass normalized modal vector at distance x Change in flexibility Bending moment of healthy beam at distance x Bending moment of delaminated beam at distance x 123 J Fail. Anal. and Preven. KðxÞ K  ðxÞ D½K  Uh1 ; Uh2 ; Uh3 and Uh4 Ud1 ; Ud2 ; Ud3 and Ud4 Kh1 ; Kh2 ; Kh3 and Kh4 Kd1 ; Kd2 ; Kd3 and Kd4 Curvature of healthy beam at distance x Curvature of delaminated beam at distance x Absolute modal curvature difference Normalized Eigen vectors of healthy beam for the first, second, third and fourth modes, respectively Normalized Eigen vectors of delaminated beam for the first, second, third and fourth modes, respectively Modal curvatures of healthy beam for the first, second, third and fourth modes, respectively Modal curvatures of delaminated beam for the first, second, third and fourth modes, respectively Introduction The laminated composite structure develops microcracks, delaminations and de-bonding during manufacturing or in service. The initiation of minute crack and its progressive development proceed till it turns into either de-bonding or delamination at the later stages. Finally, failure of the structure occurs. The failure of these structures is a quiet complex phenomenon as compared to the conventional materials. Delamination is one of the major defects in laminated composites, which deteriorates the functional characteristics of the composite structures. It reduces the strength and stiffness of the composites which affects the bending and compressive load bearing capacity. It leads to variation in dynamic characteristics of the structure which adversely affect the parameters such as modal frequency, mode shapes, dynamic flexibility, modal curvature and rotation. The application of composites in aeronautical, aerospace, marine and automobiles is increasing due to their appealing features such as higher strength-to-weight ratio, low density, excellent fatigue performance, specific stiffness, corrosion resistance and lightweight. These characteristics can be tailored as per the required specification. The high strength-to-weight ratio of these materials has attracted the automotive vehicles to get fuel efficient. Presently, the composite material covers the entire interior parts of passenger cars and some of the structural parts such as suspension system, chassis, body and its frames. Nowadays, composite suspension systems are used in 123 sports utility vehicles or in light motor vehicles as it reduces the overall weight of the vehicle. In particular, the mono composite leaf spring is adopted instead of graduated leaves and it accounts to 10–20% overall weight of the vehicle. This leaf spring has to perform satisfactorily under various loading conditions such as accelerated fatigue, shock and over loading. It is expected to ensure the safety and reliability during its service, but during working it is prone to damage as a minute crack at the inter-laminar positions at initial stage leading to delamination at the later stage. In recent years, the vibration techniques have got the considerable attention in damage assessment of composites. The modal analysis has got prominent place for damage assessment through its parameters. In this paper, an effort is made to evaluate the existence, location and severity of delamination in composite leaf spring by change in modal flexibility and curvatures. The recent research studies witness various methodologies, techniques adopted for assessment of delaminations in composites through vibration parameters. Zhang et al. [1], Ihesiulor et al. [2], Zhang et al. [3] and Rezaiee-Pajand et al. [4] proposed surrogate-assisted optimization (SAO) and artificial neural network (ANN) algorithms to evaluate the location and size of delaminations on fiber reinforced composite plates, cantilever beams and laminated structures. The finite element and experimental approaches were conducted to determine the natural frequencies of the structures. The changes in natural frequencies were used by the algorithms to find the presence, location and severity of delaminations in composites. The inverse problem has been solved by ANN and SAO algorithms to predict the location and severity of delamination. The SAO method has found superior in predicting the delamination than ANN. Some of the research work witnessed on effect of delamination location and its size on natural frequencies. Hammami et al. [5] studied the effect of delamination size in a unidirectional E-glass fiber reinforced plastic beam using linear and nonlinear vibration responses. Linear vibration analysis showed the reduction in natural frequency with de-bonding length, whereas nonlinear vibration showed the frequency shift with increased excitation amplitude. The nonlinear parameters are found more sensitive to delamination than the linear parameters, whereas Yang and Oyadiji [6] analyzed the effect of delamination in glass/epoxy composite beam due to concentrated mass loading on modal frequency variation through experimental and numerical approach. Significant change in frequencies is observed due to the concentrated mass in the delaminated region. Also, Tate et al. [7] presented the effect of length of delamination location on natural frequency of glass fiber laminated composite J Fail. Anal. and Preven. cantilever beam with glued piezoelectric sensor on the surface. It has been observed that natural frequency decreases with the increase in delamination length. Additionally, there are research works which focused also on the effect of delamination over the mode shapes of the composite structure. Chawla and Ray-Chaudhuri [8] analyzed the influence of delamination on modal properties of single and doubly curved composite plates. The sensitivity increased from lower to higher modes due to the presence of delamination in plate. But Torabi et al. [9] studied the effect of delamination size and location laminated cross-ply composite beam by vibration response. Analytical and finite element analysis has been conducted with free and constrained mode models for the first three modes. The reduction in natural frequency is found in free mode than the constrained mode in both the analyses. The minimum change in natural frequency is noticed at lower modes and the maximum change at higher modes for the delamination located in the vicinity of mode shape. Zou et al. [10] reviewed the model-dependent methods using sensor and actuator in laminated composite beam structures to detect, locate and severity of delamination. The delamination effect over the first four mode shapes has been studied. For small delamination, the lower modes have shown no response and the higher modes found more responsive. Palazzetti et al. [11] developed a methodology for assessment of delamination in laminated composite plates using free vibration. It is applied on healthy and delaminated composite plates with varying delamination size and locations. The results have been verified by experimental and numerical methods. But Garcia et al. [12] introduced a methodology for damage diagnosis using principal components analysis (PCA) through free vibration. The effect of delamination on natural frequency change observed was very small and is found not suitable for detection. The changes in first two PCs were used as a damage indicator. Liu et al. [13] also developed an analytical approach for delaminated beams to analyze the effect of edge crack on vibration parameter. Using the rotational spring model with free and constrained modes has been studied. The reduction in natural frequency has provoked by increased crack depth. The change in natural frequencies varied from maximum to minimum due to the crack movement from one side region of delamination to other side depending on the type of constraint. The studies also found using curvature mode shapes for delamination detection along with sensor and actuators. Gaudenzi et al. [14] proposed the structural health monitoring routine for the delamination detection in carbon fiber reinforced plates. The numerical analysis is conducted to determine the curvature mode shapes of plates for proper positioning of piezoelectric sensors and actuators. Wavelet packets transform (WPT)-based algorithm was applied to get vibration behavior of the plates. Linear discriminant analysis (LDA) also applied to boost the identification of delamination process, and the delamination detection process is found accurate and cost-effective. Esmaeel and Taheri [15] framed a methodology for detection of delamination in composite beam. The vibration signatures of composite structure were captured by piezoelectric sensors. The finite element simulation and advanced experimental adoptive signal processing techniques were used for the delamination detection. Qiao et al. [16] evaluated the delamination detection of E-glass/epoxy composite plate using piezoelectric sensors and actuators. Numerical and experimental approaches were conducted to detect the presence, location and delamination size. Simplified gapped smoothing method, generalized fractal dimension and strain energy method algorithms were used for extraction of curvature mode shapes. Experimental and numerical modal analysis results showed the closure approximation. Xu et al. [17] suggested the complex twodimensional wavelet curvature mode shape method for in situ evaluation of the presence and location of delamination in carbon fiber laminated plate. Numerical and experimental results showed the effectiveness of assessment of the delamination presence and location under noisy conditions. Ooijevaar et al. [18] proposed a methodology for damage identification in two advanced composite skin stiffener structures before and after impact damage by vibration techniques. In order to detect, localize and roughly quantify the damage, mode shape curvatures and modal strain energy damage index algorithms were combined for analysis. This methodology failed to identify the impact damage at the skin in between the stiffeners but is effective for health monitoring of skin stiffener connections. Yang et al. [19] presented the detection of delamination in composite beam and plate using modal flexibility curvature matrix. The natural frequency and mode shapes have been determined by experimental modal and finite element analysis. It has been observed that the presence of single or multiple delaminations and their locations were detected precisely using damage identification index. Nichols and Murphy [20] used polyspectral analysis of the structure vibration response for detection of delamination in composite beam. Nonlinear response of a beam due to the presence of delamination was understood by low-dimensional model. The dominant peak of polyspectra directly decides the delamination parameters. The recent updates in research literature mainly focused on delamination detections in composites based on various approaches such as inverse algorithms, sensitivity of modal frequencies, variation in modal shapes or displacements, curvature mode shapes and flexibility. Most of the studies used natural frequency as baseline data to assess the 123 J Fail. Anal. and Preven. delamination presence, location and severity using inverse algorithm. Even a few researchers used the sensors and actuators along with modal curvatures to detect the damage. No literature was observed to detect delamination of composites parts of automotive. In the paper, a robust numerical approach is proposed using modal curvature and flexibility methods to precisely evaluate the delamination presence, location and severity of composite leaf spring. Design and Manufacturing of Healthy and Delaminated Composite Leaf Spring The glass fiber reinforced plastic (GFRP) leaf spring has been designed, manufactured and replaced by existing steel leaf spring with the same specifications. This composite mono leaf spring used in passenger car has been taken for design and analysis. It has uniform width (b) of 50 mm, thickness (t) 20 mm and total length of the spring (eye to eye) 956 mm. The load applied at 560 mm from the front eye end. Figure 1 shows the two-dimensional diagram of composite leaf spring. Figure 1 shows a two-dimensional diagram of the leaf spring. Tables 1 and 2 show the specification of composite spring designed and the properties of E-glass/epoxy composite material. During manufacturing of delaminated composite leaf spring, Teflon sheet of 50 9 50 9 2 mm size is inserted into the spring in between the fiber layers at approximately 150 mm from axle seat to create artificial delaminated region. This sheet is chemically inert and insoluble in all the solvents. This area is the most stress concentrated and sensitive to the applied loads. Figures 2 and 3 show the manufactured healthy and delaminated composite leaf spring as per the specifications. Finite Element Modeling The healthy and delaminated composite leaf springs are modeled using finite element. These springs are assumed as cantilever beam and modeled with Euler–Bernoulli beam Fig. 1 Two-dimensional diagram of composite leaf spring 123 Table 1 Specifications of composite mono leaf spring Sr. no Parameter Value 1 Material E-glass/epoxy 2 Total length of the spring (eye to eye) 956 mm 3 Length of load application from front half (L) 560 mm 4 5 Camber Width (b) 125 mm 50 mm 6 Thickness (t) 20 mm 7 Inside diameter of front eye 38 mm 8 Inside diameter of rear eye 30 mm 10 Weight (W) 1.5 kg Table 2 Properties of E-glass/epoxy Sr. no. Properties Value 1 Density (Kg/mm3) 2000 2 Young’s modulus in X direction (Mpa) 45,000 3 Young’s modulus in Y direction (Mpa) 10,000 4 Young’s modulus in Z direction (Mpa) 10,000 5 Poisson’s ratio XY 0.3 6 Poisson’s ratio YZ 0.4 7 Poisson’s ratio XZ 0.3 8 Shear modulus XY (Mpa) 5000 9 Shear modulus YZ (Mpa) 3846.2 10 Shear modulus XZ (Mpa) 5000 finite element for delamination detection. For free vibration analysis, the governing equation of motion is given by   o2 y o2 xðx; tÞ o2 xðx; tÞ EI ð x Þ ¼0 þ m ð x Þ ox2 ox2 ot2 The above equation is solved to determine the natural frequency by finite element method. J Fail. Anal. and Preven. 2 Fig. 2 Healthy composite leaf spring 156 qAle 6 22l e 6 Me ¼ 420 4 54 2 13le 12 EI 6 6l e Ke ¼ 3 6 le 4 12 6le 22le 4l2e 13le 3l2e 6le 4l2e 6le 2l2e 3 54 13le 13le 3l2e 7 7 156 22le 5 22le 4l32 12 6le 6le 2l2e 7 7 12 6le 5 6le 4l2 Modeling of Delaminated Composite Cantilever Beam Fig. 3 Delaminated composite leaf spring These beams are discretized into finite elements, and the elemental mass and stiffness matrices are determined. After the assembly of all elemental mass and stiffness matrices for the whole section of the beam, natural frequencies for each mode are evaluated considering the boundary conditions. The equation of motion for ‘n’ degree of freedom of a structure is given as ½M€ x þ ½Kx ¼ 0 The generalized characteristic equation to calculate the Eigen value and Eigen vector for ‘n’ degrees of freedom is given by ½ ð K Þ  ki ð M Þ  ¼ 0 The solution for the above equation is of the form The delaminated composite beam is divided into four equal zones (elements) along its length. The thickness of zone-1, zone-2 and zone-4 is 20 mm except zone-3 (thickness 18 mm). To account for the delaminated region, the area of zone-3 of beam has been reduced. As per Euler–Bernoulli beam theory, the modification is observed in stiffness matrix of zone-3(delaminated region). The zone-3 doesn’t make any effect in the element mass matrix. Hence, it is neglected. The modal displacements 1, 3, 5, 7 and 9 are assigned at each elemental length from fixed end to free end along with modal rotations being 2, 4, 6, 8 and 10, respectively. The numerical analysis is carried out by considering modal displacements only. Figure 5 shows the details. The elemental mass and stiffness matrix for the delaminated beam by considering the consistent mass is given by 2 3 54 13le 156 22le qAle 6 4l2e 13le 3l2e 7 6 22le 7 and Me ¼ 4 54 13le 156 22le 5 420 2 4l32 2 13le 3le 22le 12 6le 12 6le 2 EI 6 6l 4l 6l 2l2e 7 e e  e 7 Ke ¼ 3 6 4 12 6le 5 le 12 6le 6le 2l2e 6le 4l2 xðtÞ ¼ Xeixt Delamination Evaluation Approaches Modeling of Healthy Composite Cantilever Beam The healthy composite beam is divided into four equal zones (elements) along its length. The thickness of the beam is same throughout the length. One end of the beam is fixed, and other end is free. The modal displacements 1, 3, 5, 7 and 9 are assigned at each elemental length from fixed end to free end along with modal rotations 2, 4, 6, 8 and 10. The numerical analysis is carried out by considering modal displacements only. Figure 4 shows the details. The elemental mass and stiffness matrix for the healthy beam by considering the consistent mass is given by To evaluate the presence, location and severity of delamination, modal curvature and the modal flexibility methods are applied on the healthy and delaminated cantilever composite beams. Modal Curvature Method There exists a direct coincidence between delamination location and modal curvature fields. The magnitude of modal curvature is directly proportional to severity of delamination. The artificial delamination at zone-3 reflects the reduction in stiffness. This leads to increase in local 123 J Fail. Anal. and Preven. Fig. 4 Healthy beam model Fig. 5 Delaminated beam model modal curvature and effective for the lower modal frequencies only. Consider a cantilever beam with EI as flexural rigidity, subjected to bending moment as MðxÞ and curvature as KðxÞ. Here, ‘x’ indicates the distance of any point from fixed end of the beam. The modal curvature at a distance x for healthy cantilever beam can be given as KðxÞ ¼ MðxÞ EI And the modal curvature at a distance x for delaminated cantilever beam can be given as K  ðxÞ ¼ M  ðxÞ EI The modal curvatures at local level for healthy and delaminated beam are computed by central difference approximation /ðj þ 1Þi  2/ji þ /ðj  1Þi l2 /ðj þ 1Þi  2/ji þ /ðj  1Þi K  ðxÞ ¼ l2 KðxÞ ¼ where i is the mode shape number, j the node number, /ji the modal displacement of node j at mode i and l the distance between nodes. The absolute modal curvature difference between the healthy and delaminated beam approximates the location of delamination D½K  ¼ ½K  ðxÞ  KðxÞ   /ðj þ 1Þi  2/ji þ /ðj  1Þi ¼ l2 dx   /ðj þ 1Þi  2/ji þ /ðj  1Þi  l2 hx Based on the higher value of curvature difference, the location of the delamination can be identified in a beam. 123 Modal Flexibility Method It utilizes the natural frequencies and mass normalized mode shapes for the determination of flexibility matrix for healthy and delaminated beams at distance x along the length of the cantilever beam. The change in flexibility among these beams decides the presence, location and severity of delamination. This method is also accurate for lower modes only. The flexibility matrix of healthy and delaminated beam at distance x is given by 1 1 X X 1 1 ½F hx ¼ Uxi UxiT ½F dx ¼ U UT 2 2 xi xi x x i i i¼1 i¼1 The change in flexibility matrix among the beams is D½F  ¼ ½"F hx ½F dx # " # 1 1 X X 1 1 T T ¼ Uxi Uxi  Uxi Uxi x2i x2i i¼1 i¼1 hx dx Here, xi is the ith natural frequency. The increase in the flexibility of corresponding element is used to detect the presence and the location of delamination. Numerical Method The presence, location and quantification or severity of delamination in a delaminated beam can be determined using modal flexibility and curvature methods in the following sections: Modal Flexibility Method The modal flexibility of both the beams is calculated in the following steps: Step 1 Calculation of assembled mass and stiffness matrix J Fail. Anal. and Preven. The assembled mass and stiffness matrices of healthy beam are given below 2  6559:766 0 13119:532  6559:766 13119:532 6  6559:766 6 K¼6 4 0 0 2 0:208 6 0:036 6 M¼6 4 0  6559:766 13119:532 0  6559:766 3 0:036 0 0 0:208 0:036 0 7 7 7 0:036 0:208 0:036 5 0 0 0:036 13119:532 6  6559:766 6 K ¼ 6 4 0 0 2 0:208 6 0:036 6 M ¼ 6 4 0 0  6559:766 11341:886 0  4782:12  4782:12 11341:886 0  6559:766 3 0:036 0 0 0:198 0:0324 0 7 7 7 0:0324 0:198 0:036 5 0 3 7 7 7  6559:766 5 6559:766 0:036 Mode shape Healthy beam (Hz) First Delaminated beam (Hz) 60.32 59.60 Second 185.43 172.32 Third 317.10 319.95 Fourth 422.48 409.10 The change in flexibility among both the beams is given below 0:104 The assembled mass and stiffness delaminated beam are given below 2 0 0 Table 3 Natural frequency of healthy and delaminated beam matrices of 0 0 3 7 7 7  6559:766 5 6559:766 D½F  ¼ ½2F hx ½F dx 0:4443 6 4:5883 ¼6 4 5:4706 1:5527 2:2895 4:5685 7:6999 8:7549 5:2733 7:6206 7:5663 6:9145 3 3:16231 8:80781 7 7  105 7:2161 5 6:5905 The increase in flexibility of corresponding element indicates the presence and location of delamination. Modal Curvature Method 0:104 Step 2 Determination of Eigen values and Eigen vectors The determination of Eigen values and Eigen vectors of healthy and delaminated beam is computed using MATLAB programming up to the first four mode shapes. Table 3 shows the detail. Step 3 Determination of dynamic flexibility of healthy and delaminated beam The location of delamination is found over the modeled delaminated cantilever beams after mass normalization. The mass normalized Eigen vectors of healthy beam are given as follows: 2 3 2 3 0:059 0:110 6 0:109 7 6 0:084 7 7 6 7 Uh1 ¼ 6 4 0:142 5 Uh2 ¼ 4  0:045 5 0:154  0:119 2 3 2 3 0:084  0:027 6  0:064 7 6 0:051 7 7 6 7 Uh3 ¼ 6 4  0:035 5 Uh4 ¼ 4  0:066 5 0:091 0:071 The flexibility matrices of healthy and delaminated beam are calculated after mass normalization 2 3 12:4657 13:6195 10:7133 9:96231 6 15:3183 25:4085 23:5306 21:45781 7 7 ½F hx ¼ 6 4 11:6406 23:5299 36:9363 37:0261 5 7:5327 21:4249 36:9845 50:7105 5  10 2 3 12:91 11:33 5:44 6:8 6 10:73 20:84 15:91 12:65 7 5 7 ½F dx ¼ 6 4 6:17 15:83 29:37 29:81 5  10 5:98 12:67 30:07 44:12 The mass normalized Eigen vectors of delaminated beam are given as follows: 2 3 2 3 2 3 0:047 0:108 0:091 6 0:088 7 6 0:099 7 6  0:073 7 7 6 7 6 7 Ud1 ¼ 6 4 0:126 5 Ud2 ¼ 4  0:05 5 Ud3 ¼ 4  0:035 5 0:136  0:11 0:08 2 3  0:026 6 0:045 7 7 Ud4 ¼ 6 4  0:063 5 0:074 Step 4 Dynamic flexibility change for healthy and delaminated beam The modal curvature of healthy and delaminated beam for all four nodal points is found by central difference approximation 123 J Fail. Anal. and Preven. 2 3 2 3  4:59  69:39 Kh1 ¼ 4  8:67 5  107 Kh2 ¼ 4  52:55 5  107  28:06 2 10:7 3  118:37 Kh3 ¼ 4 90:31 5  107 2 49:49 3 53:57 Kh4 ¼ 4  99:49 5  107 129:59 2 3 2 3 3:06 59:69 Kd1 ¼ 4 1:53 5  107 Kd2 ¼ 4 71:43 5  107 14:29 2 3 245:4 3 130:1 49:49 Kd3 ¼ 4 103:06 5  107 Kd4 ¼ 4 91:33 5  107 43:37 125 The absolute modal curvature difference of healthy and delaminated beam approximates the location of delamination for all four modes 2 3  1:53 D½K 1 ¼ ½Kd1  Kh1  ¼ 4 7:14 5  2 3:59 3 9:7 D½K 2 ¼ ½Kd2  Kh2  ¼ 4  18:88 5 17:34 2 3  11:73 D½K 3 ¼ ½Kd3  Kh3  ¼ 4 12:75 5  6:12 3 2  4:08 D½K 4 ¼ ½Kd4  Kh4  ¼ 4 8:16 5  4:59 where D½K 1 , D½K 2 , D½K 3 and D½K 4 are the absolute modal curvature differences for the first four mode shapes. Results and Discussion The artificial delamination inspections have been carried out in the following sections: Delamination Presence The presence of the delamination in a delaminated composite leaf spring is analyzed based on the change in modal natural frequency. The lower modes are used for the detection of delamination. The conformation of the presence of delamination is made at the global level of the delaminated spring in consultation of the natural frequency of healthy leaf spring. The reduction in natural frequency is observed in the delaminated leaf spring. This indicates the presence of delamination. Figures 6 and 7 show 123 Fig. 6 Healthy leaf spring comparison of frequency with mode number for healthy and delaminated leaf springs obtained by analytical and Optistruct solver. Delamination Location The location of delamination is found using change in modal flexibility and modal curvature difference based on comparison of both the springs. The maximum modal flexibility change is found between the portions of the beam 280–420 mm, and the maximum modal curvature is found between the portions of the beam 280–420 mm. This portion (zone-3) is the region of the delamination. Figures 8 and 9 show the details. Delamination Quantification The quantification of delamination is measured in the form of modal characteristics such as modal flexibility and modal curvatures. The maximum severity of delamination is found to be 20.48% by modal flexibility method at the seventh nodal point, and the maximum severity of delamination is found to be 466.66% at the same nodal point by modal curvature method as well for the lowest mode. This trend has been continued in the rest of the mode shapes. This indicates the severity in delamination is observed at the zone-3. Figures 10 and 11 show the details. J Fail. Anal. and Preven. Fig. 7 Delaminated leaf spring Fig. 8 Modal flexibility method Conclusion The presence, location and quantification of delamination in a composite leaf spring have been performed by modal flexibility and curvature mode shape techniques successfully. The reduction in natural frequency is observed in the delaminated spring at global level. It is the indication of delamination in a leaf spring. Using the modal flexibility method, the maximum change in flexibility is found at the third element of the beam (zone-3). On the other hand, the Fig. 9 Modal curvature method Fig. 10 Modal flexibility method maximum difference in absolute modal curvature is found at same element of the leaf spring by modal curvature method. Therefore, two independent modal approaches precisely located the delamination in a leaf spring. This identifies the location of delamination in a spring. The curvature mode shape method is found more precise in locating the delamination than the modal flexibility method. 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