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Simulation of low velocity impact on composite laminates with progressive failure analysis
Composite Structures 103 (2013) 75–85
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Simulation of low velocity impact on composite laminates with progressive failure analysis L. Maio ⇑, E. Monaco, F. Ricci, L. Lecce University of Naples ‘‘Federico II’’, Aerospace Engineering Department, Via Claudio, 21, 80125 Naples, Italy
a r t i c l e
i n f o
Article history: Available online 14 March 2013 Keywords: Composite material Low velocity impact Delamination Model
a b s t r a c t The impact is particularly damaging in the case of composites where the fibers are elastic and brittle as well as the matrix when compared with conventional ductile metals. This paper deals with the prediction of the delamination damage induced by low velocity impact in a laminated composite performed using the progressive damage model MAT162 implemented in the transient non-linear finite element code LSDYNA. Good agreement with the experimental result was observed, especially for shape and orientation of the delaminations. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Recent developments in the aviation industry to improve fuel efficiency and extent of the flight autonomy have accelerated the interest in the use of advanced composites as primary structural materials. Composite materials offer the possibility to design stiffness and strength characteristics of the final structure by suitably selecting the type of reinforcing fibers and the distribution of the reinforcing directions and allow to adapt these features as a function of the applied loads and structural requirements. They are being used for decades in transport airplane components Fig. 1. Prior to the mid-1980s, composite materials were used in transport category airplanes in secondary structures (e.g. wing edges) and control surfaces. The A320, introduced by Airbus in 1988, was the first airplane in production with an all-composite tail section; afterwards, in 1995, the commercial airplane 777, introduced by Boeing Company, was also with a composite tail section. In recent years, manufacturers have expanded the use of composites to the fuselage and wings because these materials are typically lighter and more resistant to corrosion than metallic materials that have been used traditionally in airplanes. In 2009, the Boeing 787 Dreamliner has become the first mostly composite large transport airplane in commercial service; it is about 50 percent composite by weight (excluding the engines); this airplane will be probably followed soon by the Airbus A350, having composite material roughly in the same proportion as its Boeing competitor [1].
⇑ Corresponding author. E-mail addresses: [email protected] (L. Maio), [email protected] (E. Monaco), [email protected] (F. Ricci), [email protected] (L. Lecce). 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.02.027
Some concerns have been raised related to the use of large proportion of composite on an airplane structure. These concerns mainly originated from the state of the science underpinning the expanded use of composite materials in commercial transport category airplanes, and the lack of experience with such design. The Government Accountability Office (GAO) studied how the US Federal Aviation Administration (FAA) and the European Aviation Safety Agency (EASA) certificated the 787. The GAO identified four concerns: limited information on the behavior of airplane composite structures; technical issues with the materials’ unique properties; standards for repairs; and training and awareness. The GAO also found challenges related to the damage detection of in composite materials. ‘‘Impact damage to composite structures is unique in that it may not be visible or may be barely visible, making it more difficult for a repair technician or aviation worker to detect than damage’’ the GAO said [2,3]. Impact induced damage is a very complicated phenomenon. It requires a understanding of the basic mechanics and damage mechanism. For the predictability of the composite material behavior under low velocity impact, there is a need for better models reproducing the exact physics of failure mechanism. The impact behavior of composite materials has been studied experimentally by many authors [4–7]. Several researchers have proposed analytical formulations for the prediction of the impact damage on composite laminates. However, the complexity of the physical phenomena, which includes dynamic structural behavior and loading, contact, friction, damage and failure, often results in a oversimplification of the problem which limits the analytical models. Other authors as Choi and Chang [8], Finn and Springer [9], De Moura and Gonçalves [10], Li et al. [11], Allix and Blanchard [12] or most recently Kim et al. [13], Zhou et al. [14], Wang et al.
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[15], have studied the impact on composite structures, in the form of laminated or sandwich structure, event numerically by finite element analyses, obtaining remarkable results in terms of damage prediction, as fiber breakage, matrix cracking and interlaminar delamination. So, although different approaches for analysis of impact events are available, FE analyses provide the most detailed information on the spatial and temporal distribution of damage during impact; the numerical approach by means of FE method is a more flexible and powerful alternative to the analytical formulations. However a lot of work is still necessary to improve the modeling of the damage developing during impact on composite laminates to better assess numerically their residual mechanical characteristics in order to optimize their design [16]. In this investigation, composite laminated structures subjected to low velocity impact have been analyzed using recent modeling technique; a qualitative study of the effects of lowvelocity impacts on interlaminar interface, in terms of delamination damage, of a fiber epoxy-matrix composite in cross-ply configuration is performed using finite element software LS-DYNA with implemented material model MAT162 based on damage mechanics theory and the damaged zone shape, that is delaminated area, is discussed. 2. Impact event Testing has shown that composite materials are sensitive to many aspects of in-service use for which it is difficult to provide design data. For structures submitted to under out-of-plane loading or minor objects drop, like tools during assembly or maintenance operation, composite laminates reveal a brittle behavior and can undergo significant damages. These damages are classically divided in two parts [17]: The intralaminar damages, i.e. the damages developing inside the ply like matrix cracking, fiber/matrix debonding or fibers breakages. The interlaminar damages, i.e. the damages developing at the interface between two consecutive plies, namely delamination. Particularly, low-velocity impact can leave very little visible mark onto the impacted surface and it can easily produce even delaminations and matrix cracks that may be invisible (see Fig. 2) on the surface of the laminates [18]. Furthermore, the damages are particularly dangerous because they drastically reduce the residual mechanical characteristics of the structure; for example, impact-induced damage has been shown to reduce compression strength. The reduction in compression after impact (CAI) strength due to the low velocity impact is of particular concern to the aerospace industry, both military and civil. Generally the loss in strength may be up to 60% of the undamaged value and typically industrial designers cope with this by limiting compressive strains to the range of 3000 to 4000le [19]. This significant reduction in design allowables is also a result of the fact that, at today, it is not possible to simulate the impact damage correctly. Testing coupons will not simulate the behavior of larger realistic structures because their dynamic response to low velocity impact may be quite different and it is not economic to perform impact tests on relatively large panels so as to evaluate impact behavior and damage development. For the above reasons there is a clear need for a modeling tool which avoids such blanket limitations and addresses the real nature of the damage and the physics of the failure mechanisms when a realistic structure is subjected to impact. The residual compressive strengths and impact results for a typical impacted specimen before and after CAI strength test are
Table 1 Impact, CAI and OHC test results ([45/45/0/90]3s – IM7/8552) [19]. Impact results
Compressive failure strengths (MPa)
Incident energy (J) Peak force (kN) a/W CAI
17.8
18.2
18.7
9.7 0.13 280
10.1 0.17 243
10.3 0.18 242
Open hole Unimpacted
271 685
–
229
a = Width of impact damaged area; W = laminate width, 100 mm.
shown in Table 1. The compressive strengths of unimpacted plain specimens and open hole specimens (for the latter, the observed impact damage is replaced with an equivalent open hole) measured to provide reference values are also present in the table. It can be seen that the residual strengths are reduced up to 64% of the unimpacted compressive strength between an energy level of 17.8 J and 18.7 J. (See Figs. 1 and 2). In addition to the compressive strength, the impact damage can decrease also the fatigue strength of a composite [20]. The reductions in fatigue life under 40% and 45% stress levels are shown in Fig. 3, respectively, where tension-compression fatigue tests were performed on impacted and unimpacted [0/45/90/45]ns (n = 2,4,6) laminates made of carbon/epoxy unidirectional prepreg T300/976. The low velocity impact damage in laminated composite plate structures can be recognized as a debilitating threat; it have a significant effect on the strength and durability of the laminates; it is an inevitable event, so it must be countered by appropriate design solutions. 3. Damages from low Velocity impact Composite structure failure is often caused by the development of different damage mechanisms which begin locally. Particular damage modes depend upon the type of loading, geometry, boundary conditions and stacking sequence of the composite structure. For effective predictive capabilities, all mechanisms of failure must be taken into account. In fiber-reinforced laminates, delamination is the most commonly observed damage mode; it is one of the primary concerns in the current design with composite materials and one of the key factors differentiating fiber-reinforced laminate behavior from that of metallic structures. Delamination is caused by high interlaminar stresses and relatively low interlaminar strengths of such composites in conjunction with the typically very low through-thickness strength. The phenomenon arises because fibers lying in the plane of a laminate do not provide reinforcement through the thickness, and so the composite relies on the relatively weak matrix to carry loads in that direction. The delamination occurs between layers with different fiber orientations. In fact, two adjacent laminae with different angles of the fibers introduce a mismatch of flexural and extensional rigidity that combined with the low resistance of the matrix, making the composite material is very sensitive to the delamination of these interfaces. For this reasons, a major source of delamination damage is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies (shear or bending cracks) and delaminations then grow from these cracks at the ply interfaces; infact, the delamination rarely occurs as an independent damage mode and it is almost always triggered by other damage modes such as matrix cracking; in particular, when a shear or bending crack in a layer reaches an interface between two layers oriented in different ways it is unable to easily penetrate the upper layers and it can only spread like delamination.
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Fig. 1. Sources: GAO analysis of information from FAA, NASA, Boeing Company, ‘‘Jane’s All the World’s Aircraft’’ and ‘‘Jane’s Aircraft Upgrades’’ [1–3].
Fig. 2. Edge view of impacted specimen showing extensive delamination but with no surface damage [18].
In the past years, many researchers focused their interests on impact induced damages. Wu and Springer [21] investigated the internal damage in 16 plies graphite/epoxy composites with various ply orientations. They found that the delaminations only occur when there is a change in ply orientations and that the shape of the delamination is oblong and nearly parallel to the direction of fibers in the lower ply of the interface, as shown in Fig. 4. Guynn and O’Brien [22] conducted low velocity impact tests on quasi isotropic graphite/epoxy panels of varying thickness using a 0.5 in. diameter aluminum impactor. They investigated the size, shape and distribution of delaminations utilizing several evaluative techniques. They found that the delaminations were ‘‘peanut’’ shaped at almost
every interface through-the-thickness, see Fig. 4. Several additional studies [23–26] have revealed the characteristic ‘‘peanut’’ shape delamination reported by Guynn and O-Brien. The delamination of the peanut shape is of particular interest here and will be only considered in the present study. Choi and Chang [26] had investigated the impact damage by using a line-nose impactor and summarized the impact damage mechanism as follows: intraply matrix cracks due to shear or bending initiate the damage; this type of cracks propagate into the nearby interface and cause the delamination damage between dissimilar plies; a shear matrix crack located in the inner plies of the laminate can generate a substantial delamination; a bending matrix crack located at the surface ply generates a delamination along the first interface of the cracked ply. Although the damage mechanism of point-nose impact is much more complicated than line-nose impact, the observations above about the damage process are still applicable. The sequence of impact damage in composite laminate can be classified into two stages: (1) bending or shear stresses initiate the micro cracks in matrix, (2) propagation of the micro cracks into the nearby interface yields to the delamination. So, the two kinds of damage, matrix crack and delamination, are connected (see even
Fig. 3. Reduction in fatigue life as a result of low-energy impact under 45% (on the left) and 40% (on the right) stress levels [20].
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Fig. 4. Illustration of delamination [21] and typical damage sequence through-the-thickness [22].
Fig. 5) and the relationship between matrix crack and delamination is responsible for the damage mechanism occurring under low velocity impact. 4. Progressive failure model MAT162 Continuum damage mechanics (CDMs) concepts, originated by Kachanov [27], provide a method which can potentially determine the full range of in-plane deterioration of a composite material, from the virgin material with no damage, to the fully disintegrated material with full damage. The CDM describes the gradual reduction of the elastic properties of a material; it is an accurate framework to predict the quasi-brittle process of failure of composites, where the gradual unloading of a ply after the onset of damage is simulated by means of a material degradation model. The studies reported by William and Vaziri [28] and Van Hoof et al. [29] have shown that post-failure models of CDM can significantly improve the prediction of impact damage of composite structures. An understanding of the mechanical response and failure under three dimensional states of stress is critical to designing composites. A 3D material model based on continuum damage mechanics was developed by Yen and Caiazzo [30] and implemented into LS-
DYNA, a transient dynamic finite element program, as Material Model 162. This model was designed to model ballistic penetration of thick-section composites specially; it is described in reference [31]; however, for completeness, a brief description is provided below. The MAT162 for LS-DYNA uses a modified three-dimensional intra/inter-ply continuum damage model of Matzenmiller et al. [32] according to which the post-failure mechanisms in composite plates are characterized by a reduction in material stiffness (softening) as shown by experimental results too [33,34]. This failure model can be used to simulate fiber failure, matrix damage and delamination behavior of both unidirectional and plan wave construction, subjected to transverse impact. Furthermore, this progressive failure modeling approach is advantageous as it enables one to predict delamination when locations of delamination sites cannot be anticipated; i.e., locations of potential delamination initiation is calculated without a-priori definition of an interlaminar crack surface. Three fiber damage mechanisms are considered in MAT162: (a) damage under combined uniaxial tension and transverse shear; (b) damage under uniaxial compression; (c) damage under transverse compressive loading. Three matrix failure modes are also considered: (d) matrix failure under transverse compression; (e) damage due to tensile and shear stresses; (f) damage in
Fig. 5. Result from impact loading on cross-ply CFRP laminate specimen T700S/2500 with configuration [04/904/04] and dimensions 100 100 1.5 mm3, respectively. After impact, detected damages are: delaminations at the upper and the lower 0°/90° interfaces, shear cracks in the 90° layer and a bending crack in the lower 0° ply. The delamination at the lower 0°/90° interface was of unique peanut-shape [25].
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plane parallel to the layer plane (delamination) due to throughthe-thickness tensile and shear stresses. The model uses the modified Hashin failure criteria [35] as the loading surface to account for 3D stress effects. For delamination damage, the failure criterion is reduced to the following:
f6 r26 ¼ S2
( 2 2 2 ) Ez hez i Gyz eyz Gxz exz þ þ r 26 ¼ 0 ZT Syz0 þ SzSR Sxz0 þ SzSR ð1Þ
where for the unidirectional composite x, y and z denote the fiber, in-plane transverse and out-of-plane directions, respectively; hi are Macaulay brackets; r6 is the damage threshold for modes 6 (delamination or parallel matrix damage) and it is continuously increasing function with increasing damage; for the undamaged state, the thresholds rj for all mode damages are set to 1, and, thus, the material remains in the initial undamaged state as long as fj 1 6 0, with j = 1,.,6 (because the damage criteria are six); ZT is the transverse tensile strength in the z direction; Syz0 and Sxz0 are the interlaminar shear strengths in y–z and x–z planes, respectively. Under compressive transverse strain, ez < 0, the internal surfaces induced by matrix cracking are considered to be in full contact and the shear strengths are assumed to be dependent on the associated compressive normal strain ez, in a manner similar to Coulomb– Mohr theory, i.e.,
SzSR ¼ Ez tan uhez i
ð2Þ
where u is the Coulomb’s friction angle (equivalent to angle for internal friction). The interlaminar shear strengths are enhanced under through thickness compressive stress and decrease due to through-thickness tensile stress according to Mohr–Coulomb theory; this is in agreement with past experience that has shown improvements in ILS strength of composites if through-thickness compression is applied. With regard to the progressive damage, following the notation of classic CDM, the elastic stress–strain relation for a damaged materials:
r ¼ Ee ¼ E0 ð1 dÞ
ð3Þ
Eq. (3) indicates that the stress is always linearly proportional to the strain in terms of the elastic modulus of the damaged material. In phenomenological CDM models, the damage variables are frequently expressed as functions of macroscopic measurable variables, such as strains, and generalized strains. The exponential damage evolution law as a function of strain was proposed in MAT162 as below:
di ¼ 1 exp
1 ð1 r j Þmj mj
i ¼ 1; . . . ; 6; j ¼ 1; . . . ; 6
ð4Þ
where e is the Naperian logarithm base, mj is a coefficient for material softening property. Actually there are four parameters m to be set: m1 controls the tensile and compressive fiber failure mode in x direction, m2 controls compressive matrix failure mode in y direction, m3 is for fiber crush mode, m4 for matrix (tensile/shear damage) and delamination failure. 5. Constitutive model response A single element uniaxial stress tests was conducted to verify the constitutive response of the material model MAT162. For details on used material properties, see literature reference [26]. The predicted stress/strain curve of the cubic element subjected to monotonic tension is shown in Fig. 6; compression and shear curves were omitted because of the equivalence of the damage variables as consequence of Eq. (4). The behavior of the 1-element
Fig. 6. Reaction vs. displacement response of 1-element model.
model matches the expected response from the constitutive equation. In general, the material parameters required to describe a composite are available from various publications, including material data published by the manufacturers for various fiber/matrix combinations. However, determination of the damage exponents mj requires more attention. It is well known that it is difficult to obtain the softening response of most quasi-brittle materials including fiber reinforced composites. The softening response heavily depends on the set-up and test machines, which can lead to very scattered results. Consequently the choice of damage parameters for each mode becomes an open issue. A single solid element loaded in tension was used to observe the effect of the exponent mj on the stress– strain response of an element; the result is shown in Fig. 7. This exponent determines the brittle/ductile response of the element. Infact it can be seen that smaller values of mj make the material more ductile that is a material that absorbs more energy prior to complete damage, with significant stiffness degradation prior to failure and a more gradual loss of stiffness after failure; conversely higher values give the material more brittle behavior with little or no loss in stiffness prior to failure and full damage corresponding to zero stiffness shortly after failure. When mj ? 0 the stress–strain relationship generated by the damage model looks like an ideal elastic–plastic stress–strain relationship. These qualitative observations were used later as a guide in selecting values of the parameters mj. 6. Mesh sensitivity study Strain softening, when incorporated in a computational model, exhibits, unfortunately, undesirable characteristics; its implementation runs into difficulties because the boundary value problem becomes ill-conditioned [36]. From the mathematical viewpoint, these annoying features are related to the so-called loss of hyperbolicity in the dynamic regime (ellipticity, in the static regime) of the governing differential equation. Infact if material softening is represented simply by a falling stress–strain curve in a rate-independent continuous material, then the partial differential equations of motion or equilibrium will change characteristic type at the onset of softening, from hyperbolic to elliptic in dynamic problems and otherwise in statics. In either case, the problem will become ill-posed because of the boundary and initial conditions for one class of equations are not appropriated for the other [37]. From the numerical point of view, ill-posed strain-softening problem is manifested by pathological sensitivity of the results to the size of finite elements. The slope of the post-peak branch therefore strongly depends on the number of elements, and it approaches the initial elastic slope as the number of elements tends to infinity.
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L. Maio et al. / Composite Structures 103 (2013) 75–85 Table 2 Material property used for numerical test. Typical mechanical properties for orthotropic layers Ex Ey = Ez
txy Gxy = Gxz = Gyz XT
Fig. 7. Effect of the damage exponent m on constitutive response.
The strain localization problem was investigated in material model MAT162, as done in [37], because it has strain softening elastic constitutive relation. In order to evaluate the mesh sensitivity of the algorithm, a simple coupon test simulation shown in Fig. 8 was carried out. The dimensions of the composite virtual coupon consisted of 20 10 2 mm3 who represent a small volume of the material under uniaxial stress. The virtual coupon was discretized using four different mesh densities two of them being non-structured meshes according to Fig. 9. The composite specimen was continuously loaded in the fiber direction under displacement control to mimic a pseudo-static loading on the virtual coupon with mechanical properties given in Table 2. In Fig. 10 the resulting damage distribution is shown. For comparison purposes, the load-displacement responses for all meshes were compiled in a single graph where the dissipated energy is defined by the area underneath the force displacement curves, see Fig. 11.
100 GPa 8.11 GPa 0.3 4.65 GPa 2000 GPa
As shown in Fig. 11, the post-peak branch does not depend on the number of elements, the structural responses are almost identical ensuring the control of the energy dissipation regardless of mesh refinement and element topology; so the dissipated energy in the formation of crack is clearly mesh insensitive. The postlocalization stress-displacement response was computed correctly, the damage-based model did not present an inherent element size dependency. Any minor differences could be attributed to rounding errors within the FE code. 7. Impact simulations A numerical study was conducted to investigate the predictive capabilities of the material model MAT162, discussed above, when applied to a practical impact problem. In the present investigation, the LS-DYNA finite element software was used to calculate the transient response of the impact on composite laminates. The transient response of the impact was investigated on the basis of the following assumptions: frictionless between the impactor and composite structure; neglecting the damping effect in the composite structure; ignoring the gravity force during the impact period; rigid body for the impactor. Numerical simulations were carried out to test initially the MAT162 ability to predict the force-time history for low velocity impact on composite plate and afterwards its ability to predict both orientation and shape of delamination.
Fig. 8. Specimen geometry.
Fig. 9. Structured mesh (on the left) and non-structured mesh (on the rigth).
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Fig. 10. Failure localization for structured and non-structured mesh.
Fig. 11. Effect of mesh refinement on the structural response.
Fig. 12. Structure mesh.
Initially, an impact event with nominal incident energy level of 0.67 J imparted on carbon fiber/epoxy prepreg made of HTA/6376 was simulated; the necessary information were obtained from Ref. [26]. The specimen was struck at its central point by an spherical steel impactor of mass 0.412 kg and radius 6.35 mm. The unidirectional prepreg had the following mechanical characteristics: E11 = 140 GPa, E22 = E33 = 9.5 GPa, m12 = m13 = 0.30, v23 = 0.51, G12 = G13 = 5.8 GPa , G23 = 3.9 GPa, Xt = 2000 MPa, Xc = 1650 MPa, Yt = Zt = 70 MPa, Yc = Zc = 240 MPa, S12 = S23 = 105 MPa, S13 = 85 MPa (1 for fiber direction, 2 and 3 for transverse directions). The plate was rectangular (125 mm 75 mm) with clamped edges; it had a thickness of 1 mm and a laminate stacking sequence of [45/ 45/90/0]s. The impactor was modeled as a hemispherical rigid body with non-deformable LS-DYNA material model (MAT-RIGID), because stress–strain projectile behavior was not important; while the composite laminate was discretized with under-integrated hexahedra solid elements (ELFORM 1: constant stress solid element) in plane and one element through thickness direction for ply without defining the physical interfaces between the layers; then the material model MAT162 was assigned to laminate elements. Fig. 12 shows the finite element mesh adopted for this study, which represents a simplified model of the impact test set-up; the mesh size increased from the center toward the edges because a fine grid in the impact region of the target allows to obtain a smooth stress gradient. For proper contact definition between
impactor and laminate, automatic surface to surface contact was set between the two. The value of m4 = 0.25 was used for matrix failure and delamination damage and m1 = m2 = m3 = 4 for other damage modes. The scale value S introduced into delamination criterion, Eq. (1), to account for the stress concentration factor at the delamination front, was assigned equal to 1.0 for the whole laminate (approximation of not stress concentration effects). For the sake of simplicity, Coulomb’s friction angle was set to 20, typical value for composite material. The force time history and displacement curves are shown in Fig. 13, respectively. The displacement histories appear considerably accurate while parts of the experimental traces show a marked disagreement with the numerically predicted force histories probably because the experimental data are excessively smooth relative to the predictions of model as noted by other authors who have adopted the same Ref. [38] for test data. However, although the Ref. [5] does not show delamination in the case studied, the material model predicted a small delamination zone in agreement with studies of other authors [5], Fig. 14, who used in their model interface elements to predict the delamination damage; the cause of the problem is probably due to the properties of mechanical resistance used. Note that the result obtained by both approaches is very similar although the one based on MAT162 is more efficient both from the point of view of the modeling and computationally.
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Fig. 13. Force time history (a) and displacement curve (b).
Fig. 14. Delamination fringe (post isosurface mode, LS-DYNA) (a) and interface element delamination failure envelope (b) [5].
Fig. 15. Delaminations shapes of three interfaces resulting from low velocity impact simulation. In the upper left, X-Radiograph of composite laminate is shown [26]; the delamination shape is highlighted for bottom interface 90/0 with number 1.
The last part of the simulations was the study of delamination in particular its shape and orientation were assessed varying the parameters of the model. For this purpose the studies conducted by Chang and reported in Ref. [26] were the reference. The com-
posite laminates considered were an unidirectional graphite/epoxy laminate also in this case. The composite material had the following characteristics: E11 = 156 GPa, E22 = E33 = 9.09 GPa, m12 = m13 = 0.228, v23 = 0.4,
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Fig. 16. Effect of variations in the exponent, m, on the delamination predicted by the MAT162 for a [03/903/03/903/03]s T300/976 plate; m4 = 0.25 (a) and m4 = 1 (b) were the chosen values. On the right (b) , white double arrow indicates the delamination size on the left (a).
Fig. 17. Effect of variations in the shear strength in plane 1–3, S13, on the delamination predicted; S13 = 75 MPa (a) and S13 = 55 MPa (b) were the used values. On the right (b), white and yellow double arrows indicate the delamination sizes on the left (a). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
G12 = G13 = 6.96 GPa, G23 = 3.24 GPa, Xt = 1520 MPa, Xc = 1590 MPa, Yt = Zt = 45 MPa, Yc = Zc = 252 MPa, S12 = S23 = 105 MPa; the value of the shear strength in plane 23, S23, has not been widely reported in the literature, and value as 75 GPa was used. The plate was rectangular (100 mm 76 mm) with clamped minor edges; it had a thickness of 2.16 mm and a laminate stacking sequence of [03/ 903/03/903/03]s. For the other parameters initially the following values were considered: m4 = 0.25 for matrix failure and delamination damage (ductile matrix), m1 = m2 = m3 = 4 for other damage modes, S = 1.0 as scale value; / = 20 as Coulomb’s friction angle. The impactor was a spherical body in steel of radius 6.35 mm and mass 0.16 Kg with velocity equal to 6.7 m/s. The modeling performed was the same as the previous case analyzed; both the plate and the impactor were modeled with 8-node brick elements with single integration point; there were 15 layers of elements through the thickness. As reported in Ref. [26], multiple delaminations occured in the laminates as the impactor’s velocity reached 6.7 m/s. Three delaminations were found which were also confirmed by a X-Radiograph taken from a cross-section of a sliced specimen. No delamination was found from the first 03/903 interface; there was an inner conical region immediately below the impact point with absence of damages and the most likely reason for this is the high throughthickness compressive forces during the impact event that prevent delamination damage from occurring. The delamination which occurred at the last interface appeared earlier than the others. Each delamination oriented itself along the fiber direction of the bottom ply of the delaminated interface. The overall pattern of damage were similar to that seen in other carbon fiber reinforced composites. The material model MAT162 provided a good prediction both of the delamination peanut shapes, who area characteristic of the
interface damage caused by impact loading in fiber-reinforced composite laminates, and of their orientations, as shown in Fig. 15. An analysis of the main parameters governing the delamination (i.e. m4, the interlaminar shear strength, the scale factor S and the Coulomb’s friction angle /) was then conducted and parameter effects on the interface damage farther from the region of impact were analyzed. The primary factor determining composite delamination resistance is the toughness of the resin matrix. More ductile resins provided greater delamination resistance and structural integrity in the composites [39,40]. To check numerically the parameter effect m4 governing material softening in delamination damage mode, the values of m4 representing two distinctly different responses, namely, a tough behavior for m4 = 0.25 and a little more brittle behavior for m4 = 1, were considered. In the Fig. 16 it is possible to observe that high values of the parameter extend the area delaminated. It is anticipated that the effect of this parameter on delamination damage compared to the other parameters was the most important, for this reason determination of the damage exponents m4 requires more attention. The interlaminar shear strength of a unidirectional fiber-reinforced polymer–matrix composite is a fundamental material property that is a limiting design characteristic and an important parameter in determining the ability of a composite material to resist delamination. An accurate determination of its value, therefore, is important. The interlaminar shear strength is defined as the shear stress at rupture, where the plane of fracture is located between the layers of reinforcement of a composite laminate. The S13, shear strength in the through-thickness and fiber plane which typically has a lower value than the other shear resistances for unidirectional
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Fig. 18. Effect of variations in the scale value S (upper right) and Coulmb’s friction angle (lower right), respectively.
composite, appears in the delamination criterion; it is a parameter governing delamination extension mainly along its major axis, Fig. 17. For purposes of the simulation was adopted a typical value taken from literature and the results obtained by varying it demonstrate the importance of its value. The scale factor for delamination criterion S (similar to the stress concentration factor), introduced to provide better correlation of damage area with experiments, can be determined by fitting the analytical prediction to experimental data. The increase of its value (S > 1) can induce stress concentrations that spread the damage at the delamination fronts, but without its extension in width and height resulting in loss of peanut shape and damage at the other interfaces not previously affected (in this case the one nearest to the impact area), Fig. 18. Otherwise the increase in the Coulomb’s friction angle / produces a damage reduction in the central area of panel because it enhances the shear resistances that are the main causes of delamination onset. The region on the centre line of the impactor is a low shear region, and in a state of through-thickness compression, so delamination will not start here [39]. Finally a brief discussion of energetic nature should be addressed. During low velocity impact, the impactor kinetic energy is transferred to the laminate and absorbed through the various damage mechanisms, thereby increasing the internal energy of the system. However, part of the energy given to the panel is also dissipated to counteract the ‘‘hourglassing’’. In fact the use of the reduced-integration scheme or under-integrated solid formulation, ELFORM = 1, has a drawback: it can result in mesh instability due to the nonphysical mode development of deformation called hourglass modes or zero-energy modes. Due to the simplifications in the evaluation of the element strain-displacement matrix, certain deformation modes result in a zero-strain calculation i.e. they do not cause any strain and, consequently, do not contribute to the energy integral and no stresses and nodal forces are calculated. It behaves in a manner that is similar to that of a rigid body mode. It is important to inhibit these hourglass modes by internally calculating and applying counteracting forces, but in a prudent manner so as to not significantly dissipate energy. The ‘hourglass energy’ is the undesirable dissipated
Fig. 19. Energy data (hourglass control type 4).
energy namely the work done by the ‘hourglass forces’ (that are nodal forces) introduced numerically in order to counteract the hourglass modes (minimizing distortion of the elements). For low velocity impacts, the recommendation for relatively stiff materials, e.g. composites, is to use stiffness-based hourglass formulation 4 with an hourglass coefficient of 0.05 or less that can be set via the CONTROLHOURGLASS card in LS-DYNA. In this work, Hourglass (HG) type 4 (QM = 0.03) was used. Hourglass control type 4 introduces hourglass forces, proportional to the displacements contributing to the hourglass modes, that counteract the accumulated hourglass deformation. Because of inherent stiffening effect of a stiffness-based hourglass control, it is recommended the reduction in the hourglass coefficient so as to reduce this effect. In more detail, the hourglass energy should be small relative to peak internal energy. A quick visual check can be made, in LSDYNA, from the glstat data by plotting internal energy and hourglass energy on the same graph. The rule-of-thumb is that hourglass energy should be less than 10% of the peak internal energy and this condition is verified in simulations conducted, Fig. 19.
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8. Conclusions An assessment of progressive failure model MAT162, part of the FE commercial software LS-DYNA, in predicting the delamination damage induced by low velocity impact was carried out. Finite element models were generated using only solid elements without the definition of physical interfaces between different plies. Through comparisons with impact experimental test results available in literature [26], the delamination prediction was found to be in very good agreement in terms of shape and orientation (see Fig. 15). The characteristic peanut shaped damages were observed by simulation results and they were also oriented at the correct direction. Further studies were then conducted on model parameters governing the delamination to understand their effects on the interface damage. The proposed material model provides an example of the broad spectrum of applications of Continuum Damage Mechanics to composites and the discussion is by no means intended to be a comprehensive review of such applications; so the purpose of this paper is to demonstrate a current procedure based on finite element method in predicting the non-penetrating impact response of laminated composite plates. References [1] Jackson PA, Hunter J, Daly M, Jane’s All the World’s Aircraft 2012/2013. Jane’s Information, Group; 2012. [2] Flight International, 1–7 November; 2011. [3] Status of FAA’s Actions to oversee the safety of composite airplanes, GAO-11849, September 21; 2011. [4] Finn SR. Composite Plates Impact Damage: An Atlas. CRC Press; 1991. [5] Abrate S. Impact on Composite Structures. Cambridge: University Press; 1998. [6] Davies GAO, Zhang X. Impact damage prediction in carbon composite structures. Int J Impact Eng 1995;16(1):149–70. [7] Reid SR, Zhou G. Impact Behaviour of Fibre-reinforced Composite Materials and Structures. CRC Press; 2000. [8] Choi HY, Chang FK. A model for predicting damage on graphite/epoxy laminated composites resulting from low-velocity point impact. J Compos Mater 1992;26(14):2134–69. [9] Finn SR, Springer GS. Delamination in composite plates under transverse static or impact loads – a model. Compos Struct 1993;23:177–90. [10] de Moura MFSF, Goncalves JPM. Modelling the interaction between matrix cracking and delamination in carbon–epoxy laminates under low velocity impact. Compos Sci Technol 2004;64:1021–7. [11] Li CF, Hu N, Cheng JG, Fukunaga H, Sekine H. Low-velocity impact-induced damage of continuous fiber-reinforced composites laminates. Part I. An fem numerical model. Composites Part A 2002;33:1063–72. [12] Allix O, Blanchard L. Mesomodelling of delamination: towards industrial applications. Compos Sci Technol 2006;66:731–44. [13] Kim EH, Rim MS, Lee I, Hwang TK. Composite damage model based on continuum damage mechanics and low velocity impact analysis of composite plates. Compos Struct 2013;95:123–34. [14] Zhou J, Guan ZW, Cantwell WJ. The impact response of graded foam sandwich structures. Compos Struct 2013;97:370–7. [15] Wang J, Waas AM, Wang H. Experimental and numerical study on the lowvelocity impact behavior of foam-core sandwich panels. Compos Struct 2013;96:298–311.
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[16] Wang H, Vu-Khanh T. Fracture mechanics and mechanisms of impact-induced delamination in laminated composites. J Compos Mater 1995;29:156–78. [17] Broughton WR, Mechanical testing of advanced composites, In: Hodgkinson JM editor 2000. pp. 101–4. [18] Shyr TW, Pan YH. Impact resistance and damage characteristics of composite laminates. Compos Struct 2003;62:193–203. [19] Lee J, Soutis C, Experimental investigation on the behaviour of cfrp laminated composites under impact and compression after impact (CAI). In: EKC2008 Proc. of the EU-KOREA conference on science and technology, Springer Proceedings in Physics 2008;vol, 124(2). p. 275–86. [20] Dorey G, Impact damage in composites development, consequences and prevention, In: Proc. of ICCM 6: sixth int. conf. on composite materials & ECCM 2: 2nd European Conf. on Composite Materials, London, England; 1987, [3:3.13.26]. [21] Wu HY, Springer GS. Measurements of matrix cracking and delamination caused by impact of composite plates. J Compos Mater 1988;22:518–32. [22] Guynn EG, O’Brien TK, The influence of Lay-up and thickness on composites impact damage and compression strength. AIAA/ASME/SAE, 26th structures structural dynamics and materials conference, Orlando, Florida; 1985. p. 187– 96. [23] Cordell TM, Sjoblom PO, Low velocity impact testing of composites, In: Proceedings of American society for composites, first technical conference, Dayton, Ohio; 1986. p. 297–312. [24] Liu D. Impact-induced delamination – a view of bending stiffness mismatching. J Compos Mater 1988;22:674–92. [25] Takeda S, Minakuchi S, Okabe Y, Takeda N. Delamination monitoring of laminated composites subjected to lowvelocity impact using small-diameter FBG sensors. Composites Part A 2004;36:903–8. [26] Choi HY, Chang FK. A model for predicting damage on graphite/epoxy laminated composites resulting from low-velocity point impact. J Compos Mater 1992;26(14):2l34–169. [27] Kachanov L. On the creep rupture time. Izv. Akad. Nauk SSSR 1958;8:26-31. [28] William K, Vaziri R, Finite element analysis of the impact response of CFRP composite plates. In: Proceedings of the ICCM-11 1995;5:647–54. [29] Van Hoof J, Woeswick MJ, Straznicky PV, Bolduc M, Tylko S, In: Proceedings of the 5th international LS-DYNA users conference; 1998. [30] Yen CF, Caiazzo A, Innovative processing of multifunctional composite armor for ground vehicles. ARL-CR-484, U.S. Army Research Laboratory; 2001. [31] MAT162 user reference manual; http://www.ccm.udel.edu/Tech/MAT162/ MAT162Manual_v3.pdf; 2005. [32] Matzenmiller A, Lublinear J, Taylor RL. A constitutive model for anisotropic damage in fiber-composites. Mech Mater 1995;20:125–52. [33] Ilcewicz LB, Walker TH, Murphy DP. Tension fracture of laminates for transport Fuselage, Part 4: damage tolerance analysis. In: Proceedings of the fourth NASA/DOD advanced composite tech. conf., NASA CP-3229; 1993. [34] Kongshavn I, Poursartip A. Experimental investigation of a strain softening approach to predicting failure in notched fiber reinforced composite laminates. Compos Sci Technol 1999. [35] Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34. [36] de Borst R. Some recent issues in computational failure mechanics. Int J Numer Meth Eng 2001;52:63–95. [37] Donadon MV, Iannucci L. An objectivity algorithm for strain softening material models. In: The 9th international LS-DYNA users conference; 2006. p. 15–43. [38] Iannucci L. Dynamic delamination modelling using interface elements. Comput Struct 2006;84:1029–48. [39] O’Brien TK. Characterizing delamination resistance of toughened Resin Composites. Tough Composites NASA CP 2334, Washington DC; 1984. [40] Hunston DL, Johnston NJ. Matrix resin effects in composite delamination: mode i fracture aspects, toughened composites, ASTM STP 937. Philadelphia: American Society for Testing and Materials; 1987. pp. 74– 114.
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Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Simulation of low velocity impact on composite laminates with progressive failure analysis L. Maio ⇑, E. Monaco, F. Ricci, L. Lecce University of Naples ‘‘Federico II’’, Aerospace Engineering Department, Via Claudio, 21, 80125 Naples, Italy
a r t i c l e
i n f o
Article history: Available online 14 March 2013 Keywords: Composite material Low velocity impact Delamination Model
a b s t r a c t The impact is particularly damaging in the case of composites where the fibers are elastic and brittle as well as the matrix when compared with conventional ductile metals. This paper deals with the prediction of the delamination damage induced by low velocity impact in a laminated composite performed using the progressive damage model MAT162 implemented in the transient non-linear finite element code LSDYNA. Good agreement with the experimental result was observed, especially for shape and orientation of the delaminations. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Recent developments in the aviation industry to improve fuel efficiency and extent of the flight autonomy have accelerated the interest in the use of advanced composites as primary structural materials. Composite materials offer the possibility to design stiffness and strength characteristics of the final structure by suitably selecting the type of reinforcing fibers and the distribution of the reinforcing directions and allow to adapt these features as a function of the applied loads and structural requirements. They are being used for decades in transport airplane components Fig. 1. Prior to the mid-1980s, composite materials were used in transport category airplanes in secondary structures (e.g. wing edges) and control surfaces. The A320, introduced by Airbus in 1988, was the first airplane in production with an all-composite tail section; afterwards, in 1995, the commercial airplane 777, introduced by Boeing Company, was also with a composite tail section. In recent years, manufacturers have expanded the use of composites to the fuselage and wings because these materials are typically lighter and more resistant to corrosion than metallic materials that have been used traditionally in airplanes. In 2009, the Boeing 787 Dreamliner has become the first mostly composite large transport airplane in commercial service; it is about 50 percent composite by weight (excluding the engines); this airplane will be probably followed soon by the Airbus A350, having composite material roughly in the same proportion as its Boeing competitor [1].
⇑ Corresponding author. E-mail addresses: [email protected] (L. Maio), [email protected] (E. Monaco), [email protected] (F. Ricci), [email protected] (L. Lecce). 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.02.027
Some concerns have been raised related to the use of large proportion of composite on an airplane structure. These concerns mainly originated from the state of the science underpinning the expanded use of composite materials in commercial transport category airplanes, and the lack of experience with such design. The Government Accountability Office (GAO) studied how the US Federal Aviation Administration (FAA) and the European Aviation Safety Agency (EASA) certificated the 787. The GAO identified four concerns: limited information on the behavior of airplane composite structures; technical issues with the materials’ unique properties; standards for repairs; and training and awareness. The GAO also found challenges related to the damage detection of in composite materials. ‘‘Impact damage to composite structures is unique in that it may not be visible or may be barely visible, making it more difficult for a repair technician or aviation worker to detect than damage’’ the GAO said [2,3]. Impact induced damage is a very complicated phenomenon. It requires a understanding of the basic mechanics and damage mechanism. For the predictability of the composite material behavior under low velocity impact, there is a need for better models reproducing the exact physics of failure mechanism. The impact behavior of composite materials has been studied experimentally by many authors [4–7]. Several researchers have proposed analytical formulations for the prediction of the impact damage on composite laminates. However, the complexity of the physical phenomena, which includes dynamic structural behavior and loading, contact, friction, damage and failure, often results in a oversimplification of the problem which limits the analytical models. Other authors as Choi and Chang [8], Finn and Springer [9], De Moura and Gonçalves [10], Li et al. [11], Allix and Blanchard [12] or most recently Kim et al. [13], Zhou et al. [14], Wang et al.
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[15], have studied the impact on composite structures, in the form of laminated or sandwich structure, event numerically by finite element analyses, obtaining remarkable results in terms of damage prediction, as fiber breakage, matrix cracking and interlaminar delamination. So, although different approaches for analysis of impact events are available, FE analyses provide the most detailed information on the spatial and temporal distribution of damage during impact; the numerical approach by means of FE method is a more flexible and powerful alternative to the analytical formulations. However a lot of work is still necessary to improve the modeling of the damage developing during impact on composite laminates to better assess numerically their residual mechanical characteristics in order to optimize their design [16]. In this investigation, composite laminated structures subjected to low velocity impact have been analyzed using recent modeling technique; a qualitative study of the effects of lowvelocity impacts on interlaminar interface, in terms of delamination damage, of a fiber epoxy-matrix composite in cross-ply configuration is performed using finite element software LS-DYNA with implemented material model MAT162 based on damage mechanics theory and the damaged zone shape, that is delaminated area, is discussed. 2. Impact event Testing has shown that composite materials are sensitive to many aspects of in-service use for which it is difficult to provide design data. For structures submitted to under out-of-plane loading or minor objects drop, like tools during assembly or maintenance operation, composite laminates reveal a brittle behavior and can undergo significant damages. These damages are classically divided in two parts [17]: The intralaminar damages, i.e. the damages developing inside the ply like matrix cracking, fiber/matrix debonding or fibers breakages. The interlaminar damages, i.e. the damages developing at the interface between two consecutive plies, namely delamination. Particularly, low-velocity impact can leave very little visible mark onto the impacted surface and it can easily produce even delaminations and matrix cracks that may be invisible (see Fig. 2) on the surface of the laminates [18]. Furthermore, the damages are particularly dangerous because they drastically reduce the residual mechanical characteristics of the structure; for example, impact-induced damage has been shown to reduce compression strength. The reduction in compression after impact (CAI) strength due to the low velocity impact is of particular concern to the aerospace industry, both military and civil. Generally the loss in strength may be up to 60% of the undamaged value and typically industrial designers cope with this by limiting compressive strains to the range of 3000 to 4000le [19]. This significant reduction in design allowables is also a result of the fact that, at today, it is not possible to simulate the impact damage correctly. Testing coupons will not simulate the behavior of larger realistic structures because their dynamic response to low velocity impact may be quite different and it is not economic to perform impact tests on relatively large panels so as to evaluate impact behavior and damage development. For the above reasons there is a clear need for a modeling tool which avoids such blanket limitations and addresses the real nature of the damage and the physics of the failure mechanisms when a realistic structure is subjected to impact. The residual compressive strengths and impact results for a typical impacted specimen before and after CAI strength test are
Table 1 Impact, CAI and OHC test results ([45/45/0/90]3s – IM7/8552) [19]. Impact results
Compressive failure strengths (MPa)
Incident energy (J) Peak force (kN) a/W CAI
17.8
18.2
18.7
9.7 0.13 280
10.1 0.17 243
10.3 0.18 242
Open hole Unimpacted
271 685
–
229
a = Width of impact damaged area; W = laminate width, 100 mm.
shown in Table 1. The compressive strengths of unimpacted plain specimens and open hole specimens (for the latter, the observed impact damage is replaced with an equivalent open hole) measured to provide reference values are also present in the table. It can be seen that the residual strengths are reduced up to 64% of the unimpacted compressive strength between an energy level of 17.8 J and 18.7 J. (See Figs. 1 and 2). In addition to the compressive strength, the impact damage can decrease also the fatigue strength of a composite [20]. The reductions in fatigue life under 40% and 45% stress levels are shown in Fig. 3, respectively, where tension-compression fatigue tests were performed on impacted and unimpacted [0/45/90/45]ns (n = 2,4,6) laminates made of carbon/epoxy unidirectional prepreg T300/976. The low velocity impact damage in laminated composite plate structures can be recognized as a debilitating threat; it have a significant effect on the strength and durability of the laminates; it is an inevitable event, so it must be countered by appropriate design solutions. 3. Damages from low Velocity impact Composite structure failure is often caused by the development of different damage mechanisms which begin locally. Particular damage modes depend upon the type of loading, geometry, boundary conditions and stacking sequence of the composite structure. For effective predictive capabilities, all mechanisms of failure must be taken into account. In fiber-reinforced laminates, delamination is the most commonly observed damage mode; it is one of the primary concerns in the current design with composite materials and one of the key factors differentiating fiber-reinforced laminate behavior from that of metallic structures. Delamination is caused by high interlaminar stresses and relatively low interlaminar strengths of such composites in conjunction with the typically very low through-thickness strength. The phenomenon arises because fibers lying in the plane of a laminate do not provide reinforcement through the thickness, and so the composite relies on the relatively weak matrix to carry loads in that direction. The delamination occurs between layers with different fiber orientations. In fact, two adjacent laminae with different angles of the fibers introduce a mismatch of flexural and extensional rigidity that combined with the low resistance of the matrix, making the composite material is very sensitive to the delamination of these interfaces. For this reasons, a major source of delamination damage is from low-velocity impact. In thin composite laminates under point loads, matrix cracks develop first in the plies (shear or bending cracks) and delaminations then grow from these cracks at the ply interfaces; infact, the delamination rarely occurs as an independent damage mode and it is almost always triggered by other damage modes such as matrix cracking; in particular, when a shear or bending crack in a layer reaches an interface between two layers oriented in different ways it is unable to easily penetrate the upper layers and it can only spread like delamination.
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Fig. 1. Sources: GAO analysis of information from FAA, NASA, Boeing Company, ‘‘Jane’s All the World’s Aircraft’’ and ‘‘Jane’s Aircraft Upgrades’’ [1–3].
Fig. 2. Edge view of impacted specimen showing extensive delamination but with no surface damage [18].
In the past years, many researchers focused their interests on impact induced damages. Wu and Springer [21] investigated the internal damage in 16 plies graphite/epoxy composites with various ply orientations. They found that the delaminations only occur when there is a change in ply orientations and that the shape of the delamination is oblong and nearly parallel to the direction of fibers in the lower ply of the interface, as shown in Fig. 4. Guynn and O’Brien [22] conducted low velocity impact tests on quasi isotropic graphite/epoxy panels of varying thickness using a 0.5 in. diameter aluminum impactor. They investigated the size, shape and distribution of delaminations utilizing several evaluative techniques. They found that the delaminations were ‘‘peanut’’ shaped at almost
every interface through-the-thickness, see Fig. 4. Several additional studies [23–26] have revealed the characteristic ‘‘peanut’’ shape delamination reported by Guynn and O-Brien. The delamination of the peanut shape is of particular interest here and will be only considered in the present study. Choi and Chang [26] had investigated the impact damage by using a line-nose impactor and summarized the impact damage mechanism as follows: intraply matrix cracks due to shear or bending initiate the damage; this type of cracks propagate into the nearby interface and cause the delamination damage between dissimilar plies; a shear matrix crack located in the inner plies of the laminate can generate a substantial delamination; a bending matrix crack located at the surface ply generates a delamination along the first interface of the cracked ply. Although the damage mechanism of point-nose impact is much more complicated than line-nose impact, the observations above about the damage process are still applicable. The sequence of impact damage in composite laminate can be classified into two stages: (1) bending or shear stresses initiate the micro cracks in matrix, (2) propagation of the micro cracks into the nearby interface yields to the delamination. So, the two kinds of damage, matrix crack and delamination, are connected (see even
Fig. 3. Reduction in fatigue life as a result of low-energy impact under 45% (on the left) and 40% (on the right) stress levels [20].
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Fig. 4. Illustration of delamination [21] and typical damage sequence through-the-thickness [22].
Fig. 5) and the relationship between matrix crack and delamination is responsible for the damage mechanism occurring under low velocity impact. 4. Progressive failure model MAT162 Continuum damage mechanics (CDMs) concepts, originated by Kachanov [27], provide a method which can potentially determine the full range of in-plane deterioration of a composite material, from the virgin material with no damage, to the fully disintegrated material with full damage. The CDM describes the gradual reduction of the elastic properties of a material; it is an accurate framework to predict the quasi-brittle process of failure of composites, where the gradual unloading of a ply after the onset of damage is simulated by means of a material degradation model. The studies reported by William and Vaziri [28] and Van Hoof et al. [29] have shown that post-failure models of CDM can significantly improve the prediction of impact damage of composite structures. An understanding of the mechanical response and failure under three dimensional states of stress is critical to designing composites. A 3D material model based on continuum damage mechanics was developed by Yen and Caiazzo [30] and implemented into LS-
DYNA, a transient dynamic finite element program, as Material Model 162. This model was designed to model ballistic penetration of thick-section composites specially; it is described in reference [31]; however, for completeness, a brief description is provided below. The MAT162 for LS-DYNA uses a modified three-dimensional intra/inter-ply continuum damage model of Matzenmiller et al. [32] according to which the post-failure mechanisms in composite plates are characterized by a reduction in material stiffness (softening) as shown by experimental results too [33,34]. This failure model can be used to simulate fiber failure, matrix damage and delamination behavior of both unidirectional and plan wave construction, subjected to transverse impact. Furthermore, this progressive failure modeling approach is advantageous as it enables one to predict delamination when locations of delamination sites cannot be anticipated; i.e., locations of potential delamination initiation is calculated without a-priori definition of an interlaminar crack surface. Three fiber damage mechanisms are considered in MAT162: (a) damage under combined uniaxial tension and transverse shear; (b) damage under uniaxial compression; (c) damage under transverse compressive loading. Three matrix failure modes are also considered: (d) matrix failure under transverse compression; (e) damage due to tensile and shear stresses; (f) damage in
Fig. 5. Result from impact loading on cross-ply CFRP laminate specimen T700S/2500 with configuration [04/904/04] and dimensions 100 100 1.5 mm3, respectively. After impact, detected damages are: delaminations at the upper and the lower 0°/90° interfaces, shear cracks in the 90° layer and a bending crack in the lower 0° ply. The delamination at the lower 0°/90° interface was of unique peanut-shape [25].
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plane parallel to the layer plane (delamination) due to throughthe-thickness tensile and shear stresses. The model uses the modified Hashin failure criteria [35] as the loading surface to account for 3D stress effects. For delamination damage, the failure criterion is reduced to the following:
f6 r26 ¼ S2
( 2 2 2 ) Ez hez i Gyz eyz Gxz exz þ þ r 26 ¼ 0 ZT Syz0 þ SzSR Sxz0 þ SzSR ð1Þ
where for the unidirectional composite x, y and z denote the fiber, in-plane transverse and out-of-plane directions, respectively; hi are Macaulay brackets; r6 is the damage threshold for modes 6 (delamination or parallel matrix damage) and it is continuously increasing function with increasing damage; for the undamaged state, the thresholds rj for all mode damages are set to 1, and, thus, the material remains in the initial undamaged state as long as fj 1 6 0, with j = 1,.,6 (because the damage criteria are six); ZT is the transverse tensile strength in the z direction; Syz0 and Sxz0 are the interlaminar shear strengths in y–z and x–z planes, respectively. Under compressive transverse strain, ez < 0, the internal surfaces induced by matrix cracking are considered to be in full contact and the shear strengths are assumed to be dependent on the associated compressive normal strain ez, in a manner similar to Coulomb– Mohr theory, i.e.,
SzSR ¼ Ez tan uhez i
ð2Þ
where u is the Coulomb’s friction angle (equivalent to angle for internal friction). The interlaminar shear strengths are enhanced under through thickness compressive stress and decrease due to through-thickness tensile stress according to Mohr–Coulomb theory; this is in agreement with past experience that has shown improvements in ILS strength of composites if through-thickness compression is applied. With regard to the progressive damage, following the notation of classic CDM, the elastic stress–strain relation for a damaged materials:
r ¼ Ee ¼ E0 ð1 dÞ
ð3Þ
Eq. (3) indicates that the stress is always linearly proportional to the strain in terms of the elastic modulus of the damaged material. In phenomenological CDM models, the damage variables are frequently expressed as functions of macroscopic measurable variables, such as strains, and generalized strains. The exponential damage evolution law as a function of strain was proposed in MAT162 as below:
di ¼ 1 exp
1 ð1 r j Þmj mj
i ¼ 1; . . . ; 6; j ¼ 1; . . . ; 6
ð4Þ
where e is the Naperian logarithm base, mj is a coefficient for material softening property. Actually there are four parameters m to be set: m1 controls the tensile and compressive fiber failure mode in x direction, m2 controls compressive matrix failure mode in y direction, m3 is for fiber crush mode, m4 for matrix (tensile/shear damage) and delamination failure. 5. Constitutive model response A single element uniaxial stress tests was conducted to verify the constitutive response of the material model MAT162. For details on used material properties, see literature reference [26]. The predicted stress/strain curve of the cubic element subjected to monotonic tension is shown in Fig. 6; compression and shear curves were omitted because of the equivalence of the damage variables as consequence of Eq. (4). The behavior of the 1-element
Fig. 6. Reaction vs. displacement response of 1-element model.
model matches the expected response from the constitutive equation. In general, the material parameters required to describe a composite are available from various publications, including material data published by the manufacturers for various fiber/matrix combinations. However, determination of the damage exponents mj requires more attention. It is well known that it is difficult to obtain the softening response of most quasi-brittle materials including fiber reinforced composites. The softening response heavily depends on the set-up and test machines, which can lead to very scattered results. Consequently the choice of damage parameters for each mode becomes an open issue. A single solid element loaded in tension was used to observe the effect of the exponent mj on the stress– strain response of an element; the result is shown in Fig. 7. This exponent determines the brittle/ductile response of the element. Infact it can be seen that smaller values of mj make the material more ductile that is a material that absorbs more energy prior to complete damage, with significant stiffness degradation prior to failure and a more gradual loss of stiffness after failure; conversely higher values give the material more brittle behavior with little or no loss in stiffness prior to failure and full damage corresponding to zero stiffness shortly after failure. When mj ? 0 the stress–strain relationship generated by the damage model looks like an ideal elastic–plastic stress–strain relationship. These qualitative observations were used later as a guide in selecting values of the parameters mj. 6. Mesh sensitivity study Strain softening, when incorporated in a computational model, exhibits, unfortunately, undesirable characteristics; its implementation runs into difficulties because the boundary value problem becomes ill-conditioned [36]. From the mathematical viewpoint, these annoying features are related to the so-called loss of hyperbolicity in the dynamic regime (ellipticity, in the static regime) of the governing differential equation. Infact if material softening is represented simply by a falling stress–strain curve in a rate-independent continuous material, then the partial differential equations of motion or equilibrium will change characteristic type at the onset of softening, from hyperbolic to elliptic in dynamic problems and otherwise in statics. In either case, the problem will become ill-posed because of the boundary and initial conditions for one class of equations are not appropriated for the other [37]. From the numerical point of view, ill-posed strain-softening problem is manifested by pathological sensitivity of the results to the size of finite elements. The slope of the post-peak branch therefore strongly depends on the number of elements, and it approaches the initial elastic slope as the number of elements tends to infinity.
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L. Maio et al. / Composite Structures 103 (2013) 75–85 Table 2 Material property used for numerical test. Typical mechanical properties for orthotropic layers Ex Ey = Ez
txy Gxy = Gxz = Gyz XT
Fig. 7. Effect of the damage exponent m on constitutive response.
The strain localization problem was investigated in material model MAT162, as done in [37], because it has strain softening elastic constitutive relation. In order to evaluate the mesh sensitivity of the algorithm, a simple coupon test simulation shown in Fig. 8 was carried out. The dimensions of the composite virtual coupon consisted of 20 10 2 mm3 who represent a small volume of the material under uniaxial stress. The virtual coupon was discretized using four different mesh densities two of them being non-structured meshes according to Fig. 9. The composite specimen was continuously loaded in the fiber direction under displacement control to mimic a pseudo-static loading on the virtual coupon with mechanical properties given in Table 2. In Fig. 10 the resulting damage distribution is shown. For comparison purposes, the load-displacement responses for all meshes were compiled in a single graph where the dissipated energy is defined by the area underneath the force displacement curves, see Fig. 11.
100 GPa 8.11 GPa 0.3 4.65 GPa 2000 GPa
As shown in Fig. 11, the post-peak branch does not depend on the number of elements, the structural responses are almost identical ensuring the control of the energy dissipation regardless of mesh refinement and element topology; so the dissipated energy in the formation of crack is clearly mesh insensitive. The postlocalization stress-displacement response was computed correctly, the damage-based model did not present an inherent element size dependency. Any minor differences could be attributed to rounding errors within the FE code. 7. Impact simulations A numerical study was conducted to investigate the predictive capabilities of the material model MAT162, discussed above, when applied to a practical impact problem. In the present investigation, the LS-DYNA finite element software was used to calculate the transient response of the impact on composite laminates. The transient response of the impact was investigated on the basis of the following assumptions: frictionless between the impactor and composite structure; neglecting the damping effect in the composite structure; ignoring the gravity force during the impact period; rigid body for the impactor. Numerical simulations were carried out to test initially the MAT162 ability to predict the force-time history for low velocity impact on composite plate and afterwards its ability to predict both orientation and shape of delamination.
Fig. 8. Specimen geometry.
Fig. 9. Structured mesh (on the left) and non-structured mesh (on the rigth).
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Fig. 10. Failure localization for structured and non-structured mesh.
Fig. 11. Effect of mesh refinement on the structural response.
Fig. 12. Structure mesh.
Initially, an impact event with nominal incident energy level of 0.67 J imparted on carbon fiber/epoxy prepreg made of HTA/6376 was simulated; the necessary information were obtained from Ref. [26]. The specimen was struck at its central point by an spherical steel impactor of mass 0.412 kg and radius 6.35 mm. The unidirectional prepreg had the following mechanical characteristics: E11 = 140 GPa, E22 = E33 = 9.5 GPa, m12 = m13 = 0.30, v23 = 0.51, G12 = G13 = 5.8 GPa , G23 = 3.9 GPa, Xt = 2000 MPa, Xc = 1650 MPa, Yt = Zt = 70 MPa, Yc = Zc = 240 MPa, S12 = S23 = 105 MPa, S13 = 85 MPa (1 for fiber direction, 2 and 3 for transverse directions). The plate was rectangular (125 mm 75 mm) with clamped edges; it had a thickness of 1 mm and a laminate stacking sequence of [45/ 45/90/0]s. The impactor was modeled as a hemispherical rigid body with non-deformable LS-DYNA material model (MAT-RIGID), because stress–strain projectile behavior was not important; while the composite laminate was discretized with under-integrated hexahedra solid elements (ELFORM 1: constant stress solid element) in plane and one element through thickness direction for ply without defining the physical interfaces between the layers; then the material model MAT162 was assigned to laminate elements. Fig. 12 shows the finite element mesh adopted for this study, which represents a simplified model of the impact test set-up; the mesh size increased from the center toward the edges because a fine grid in the impact region of the target allows to obtain a smooth stress gradient. For proper contact definition between
impactor and laminate, automatic surface to surface contact was set between the two. The value of m4 = 0.25 was used for matrix failure and delamination damage and m1 = m2 = m3 = 4 for other damage modes. The scale value S introduced into delamination criterion, Eq. (1), to account for the stress concentration factor at the delamination front, was assigned equal to 1.0 for the whole laminate (approximation of not stress concentration effects). For the sake of simplicity, Coulomb’s friction angle was set to 20, typical value for composite material. The force time history and displacement curves are shown in Fig. 13, respectively. The displacement histories appear considerably accurate while parts of the experimental traces show a marked disagreement with the numerically predicted force histories probably because the experimental data are excessively smooth relative to the predictions of model as noted by other authors who have adopted the same Ref. [38] for test data. However, although the Ref. [5] does not show delamination in the case studied, the material model predicted a small delamination zone in agreement with studies of other authors [5], Fig. 14, who used in their model interface elements to predict the delamination damage; the cause of the problem is probably due to the properties of mechanical resistance used. Note that the result obtained by both approaches is very similar although the one based on MAT162 is more efficient both from the point of view of the modeling and computationally.
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Fig. 13. Force time history (a) and displacement curve (b).
Fig. 14. Delamination fringe (post isosurface mode, LS-DYNA) (a) and interface element delamination failure envelope (b) [5].
Fig. 15. Delaminations shapes of three interfaces resulting from low velocity impact simulation. In the upper left, X-Radiograph of composite laminate is shown [26]; the delamination shape is highlighted for bottom interface 90/0 with number 1.
The last part of the simulations was the study of delamination in particular its shape and orientation were assessed varying the parameters of the model. For this purpose the studies conducted by Chang and reported in Ref. [26] were the reference. The com-
posite laminates considered were an unidirectional graphite/epoxy laminate also in this case. The composite material had the following characteristics: E11 = 156 GPa, E22 = E33 = 9.09 GPa, m12 = m13 = 0.228, v23 = 0.4,
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Fig. 16. Effect of variations in the exponent, m, on the delamination predicted by the MAT162 for a [03/903/03/903/03]s T300/976 plate; m4 = 0.25 (a) and m4 = 1 (b) were the chosen values. On the right (b) , white double arrow indicates the delamination size on the left (a).
Fig. 17. Effect of variations in the shear strength in plane 1–3, S13, on the delamination predicted; S13 = 75 MPa (a) and S13 = 55 MPa (b) were the used values. On the right (b), white and yellow double arrows indicate the delamination sizes on the left (a). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
G12 = G13 = 6.96 GPa, G23 = 3.24 GPa, Xt = 1520 MPa, Xc = 1590 MPa, Yt = Zt = 45 MPa, Yc = Zc = 252 MPa, S12 = S23 = 105 MPa; the value of the shear strength in plane 23, S23, has not been widely reported in the literature, and value as 75 GPa was used. The plate was rectangular (100 mm 76 mm) with clamped minor edges; it had a thickness of 2.16 mm and a laminate stacking sequence of [03/ 903/03/903/03]s. For the other parameters initially the following values were considered: m4 = 0.25 for matrix failure and delamination damage (ductile matrix), m1 = m2 = m3 = 4 for other damage modes, S = 1.0 as scale value; / = 20 as Coulomb’s friction angle. The impactor was a spherical body in steel of radius 6.35 mm and mass 0.16 Kg with velocity equal to 6.7 m/s. The modeling performed was the same as the previous case analyzed; both the plate and the impactor were modeled with 8-node brick elements with single integration point; there were 15 layers of elements through the thickness. As reported in Ref. [26], multiple delaminations occured in the laminates as the impactor’s velocity reached 6.7 m/s. Three delaminations were found which were also confirmed by a X-Radiograph taken from a cross-section of a sliced specimen. No delamination was found from the first 03/903 interface; there was an inner conical region immediately below the impact point with absence of damages and the most likely reason for this is the high throughthickness compressive forces during the impact event that prevent delamination damage from occurring. The delamination which occurred at the last interface appeared earlier than the others. Each delamination oriented itself along the fiber direction of the bottom ply of the delaminated interface. The overall pattern of damage were similar to that seen in other carbon fiber reinforced composites. The material model MAT162 provided a good prediction both of the delamination peanut shapes, who area characteristic of the
interface damage caused by impact loading in fiber-reinforced composite laminates, and of their orientations, as shown in Fig. 15. An analysis of the main parameters governing the delamination (i.e. m4, the interlaminar shear strength, the scale factor S and the Coulomb’s friction angle /) was then conducted and parameter effects on the interface damage farther from the region of impact were analyzed. The primary factor determining composite delamination resistance is the toughness of the resin matrix. More ductile resins provided greater delamination resistance and structural integrity in the composites [39,40]. To check numerically the parameter effect m4 governing material softening in delamination damage mode, the values of m4 representing two distinctly different responses, namely, a tough behavior for m4 = 0.25 and a little more brittle behavior for m4 = 1, were considered. In the Fig. 16 it is possible to observe that high values of the parameter extend the area delaminated. It is anticipated that the effect of this parameter on delamination damage compared to the other parameters was the most important, for this reason determination of the damage exponents m4 requires more attention. The interlaminar shear strength of a unidirectional fiber-reinforced polymer–matrix composite is a fundamental material property that is a limiting design characteristic and an important parameter in determining the ability of a composite material to resist delamination. An accurate determination of its value, therefore, is important. The interlaminar shear strength is defined as the shear stress at rupture, where the plane of fracture is located between the layers of reinforcement of a composite laminate. The S13, shear strength in the through-thickness and fiber plane which typically has a lower value than the other shear resistances for unidirectional
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Fig. 18. Effect of variations in the scale value S (upper right) and Coulmb’s friction angle (lower right), respectively.
composite, appears in the delamination criterion; it is a parameter governing delamination extension mainly along its major axis, Fig. 17. For purposes of the simulation was adopted a typical value taken from literature and the results obtained by varying it demonstrate the importance of its value. The scale factor for delamination criterion S (similar to the stress concentration factor), introduced to provide better correlation of damage area with experiments, can be determined by fitting the analytical prediction to experimental data. The increase of its value (S > 1) can induce stress concentrations that spread the damage at the delamination fronts, but without its extension in width and height resulting in loss of peanut shape and damage at the other interfaces not previously affected (in this case the one nearest to the impact area), Fig. 18. Otherwise the increase in the Coulomb’s friction angle / produces a damage reduction in the central area of panel because it enhances the shear resistances that are the main causes of delamination onset. The region on the centre line of the impactor is a low shear region, and in a state of through-thickness compression, so delamination will not start here [39]. Finally a brief discussion of energetic nature should be addressed. During low velocity impact, the impactor kinetic energy is transferred to the laminate and absorbed through the various damage mechanisms, thereby increasing the internal energy of the system. However, part of the energy given to the panel is also dissipated to counteract the ‘‘hourglassing’’. In fact the use of the reduced-integration scheme or under-integrated solid formulation, ELFORM = 1, has a drawback: it can result in mesh instability due to the nonphysical mode development of deformation called hourglass modes or zero-energy modes. Due to the simplifications in the evaluation of the element strain-displacement matrix, certain deformation modes result in a zero-strain calculation i.e. they do not cause any strain and, consequently, do not contribute to the energy integral and no stresses and nodal forces are calculated. It behaves in a manner that is similar to that of a rigid body mode. It is important to inhibit these hourglass modes by internally calculating and applying counteracting forces, but in a prudent manner so as to not significantly dissipate energy. The ‘hourglass energy’ is the undesirable dissipated
Fig. 19. Energy data (hourglass control type 4).
energy namely the work done by the ‘hourglass forces’ (that are nodal forces) introduced numerically in order to counteract the hourglass modes (minimizing distortion of the elements). For low velocity impacts, the recommendation for relatively stiff materials, e.g. composites, is to use stiffness-based hourglass formulation 4 with an hourglass coefficient of 0.05 or less that can be set via the CONTROLHOURGLASS card in LS-DYNA. In this work, Hourglass (HG) type 4 (QM = 0.03) was used. Hourglass control type 4 introduces hourglass forces, proportional to the displacements contributing to the hourglass modes, that counteract the accumulated hourglass deformation. Because of inherent stiffening effect of a stiffness-based hourglass control, it is recommended the reduction in the hourglass coefficient so as to reduce this effect. In more detail, the hourglass energy should be small relative to peak internal energy. A quick visual check can be made, in LSDYNA, from the glstat data by plotting internal energy and hourglass energy on the same graph. The rule-of-thumb is that hourglass energy should be less than 10% of the peak internal energy and this condition is verified in simulations conducted, Fig. 19.
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8. Conclusions An assessment of progressive failure model MAT162, part of the FE commercial software LS-DYNA, in predicting the delamination damage induced by low velocity impact was carried out. Finite element models were generated using only solid elements without the definition of physical interfaces between different plies. Through comparisons with impact experimental test results available in literature [26], the delamination prediction was found to be in very good agreement in terms of shape and orientation (see Fig. 15). The characteristic peanut shaped damages were observed by simulation results and they were also oriented at the correct direction. Further studies were then conducted on model parameters governing the delamination to understand their effects on the interface damage. The proposed material model provides an example of the broad spectrum of applications of Continuum Damage Mechanics to composites and the discussion is by no means intended to be a comprehensive review of such applications; so the purpose of this paper is to demonstrate a current procedure based on finite element method in predicting the non-penetrating impact response of laminated composite plates. References [1] Jackson PA, Hunter J, Daly M, Jane’s All the World’s Aircraft 2012/2013. Jane’s Information, Group; 2012. [2] Flight International, 1–7 November; 2011. [3] Status of FAA’s Actions to oversee the safety of composite airplanes, GAO-11849, September 21; 2011. [4] Finn SR. Composite Plates Impact Damage: An Atlas. CRC Press; 1991. [5] Abrate S. Impact on Composite Structures. Cambridge: University Press; 1998. [6] Davies GAO, Zhang X. Impact damage prediction in carbon composite structures. Int J Impact Eng 1995;16(1):149–70. [7] Reid SR, Zhou G. Impact Behaviour of Fibre-reinforced Composite Materials and Structures. CRC Press; 2000. [8] Choi HY, Chang FK. A model for predicting damage on graphite/epoxy laminated composites resulting from low-velocity point impact. J Compos Mater 1992;26(14):2134–69. [9] Finn SR, Springer GS. Delamination in composite plates under transverse static or impact loads – a model. Compos Struct 1993;23:177–90. [10] de Moura MFSF, Goncalves JPM. Modelling the interaction between matrix cracking and delamination in carbon–epoxy laminates under low velocity impact. Compos Sci Technol 2004;64:1021–7. [11] Li CF, Hu N, Cheng JG, Fukunaga H, Sekine H. Low-velocity impact-induced damage of continuous fiber-reinforced composites laminates. Part I. An fem numerical model. Composites Part A 2002;33:1063–72. [12] Allix O, Blanchard L. Mesomodelling of delamination: towards industrial applications. Compos Sci Technol 2006;66:731–44. [13] Kim EH, Rim MS, Lee I, Hwang TK. Composite damage model based on continuum damage mechanics and low velocity impact analysis of composite plates. Compos Struct 2013;95:123–34. [14] Zhou J, Guan ZW, Cantwell WJ. The impact response of graded foam sandwich structures. Compos Struct 2013;97:370–7. [15] Wang J, Waas AM, Wang H. Experimental and numerical study on the lowvelocity impact behavior of foam-core sandwich panels. Compos Struct 2013;96:298–311.
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