# Low- and medium-velocity impact as a cause of failure in polymer matrix composites

## Abstract:

This chapter gives an overview of causes and effects of damage due to low- and medium-velocity impact. Typical features of impact damage are described, with focus on tape prepreg laminates. The relation between impact response and impactor/plate mass ratio is explained and appropriate analytical response models outlined. Experimental observations of the behaviour of impact damage under load and its effect on strength and buckling are described. A brief discussion is also provided on the application of computational methods to impact on composites, and issues needing attention are highlighted. The chapter is concluded with a discussion on future trends and advice for further information.

## 3.1 Introduction

Impact damage is a prime concern in the design of composite structures, particularly in the aerospace industry, as it (i) happens easily, (ii) often is hard to detect visually and (iii) may reduce strength and stability significantly. The concentrated loads during impact induce high out-of-plane stresses that easily cause damage in composite laminates, due to their relatively low out-of-plane strength. Damage involves multiple internal delaminations and cracks, often without noticeable surface dents, which makes visual detection difficult. The multiple delaminations easily cause local buckling, which promotes global buckling and compressive failure at loads as low as one-third of the load for undamaged laminates. Cracks involving broken fibres cause stress concentrations leading to premature failure both in compression and tension. The issue of impact on composites requires consideration of a sequence of events, starting with defining the impact threat, via the impact response and the resulting generation of damage, until the eventual effect on strength and stability after impact (Fig. 3.1). Most of the associated problems are nonlinear, due to the influence of contact, damage growth and large deflections.

3.1 Issues of impact on composites. (based on Olsson *et al*., 2000)

Most composite structures experience a multitude of impact threats, that are all intrinsically unpredictable in terms of occurrence and severity. Manufacturing may involve dropping of tools or of the actual components. Aircraft in service may experience impact by hail, birds and runway debris, while dropped tools and collisions are common during maintenance. Dropped tools and road debris are also common for ground vehicles, while ships experience collisions with floating objects and impact by dropped tools and payload.

This chapter focuses on the effects of low- and medium-velocity impact. Typical features of impact damage zones are described first, followed by a description of various impact response types. Models for the different response types are then discussed, followed by a discussion on the effects of impact damage on strength and stability after impact. The chapter is concluded with a discussion on future trends and advice for further reading.

## 3.2 Impact damage

Impact damage is caused by the interaction of indentation and global deflection while pure indentation damage is observed when the panel back face is supported or when the effect of global deflection is negligible. Impact damage and indentation damage in laminates involve a number of common damage features such as matrix cracks, delaminations and fibre fracture (Fig. 3.2), although indentation damage is much more localised. Thus, indentation of thick laminates was observed to cause fibre fracture and matrix cracking within a distance of about one contact radius from the loaded surface (Poe, 1991). Impact damage in sandwich panels with laminated face sheets involves the same damage features as in plain laminates, although more localised, but in addition core crushing is almost invariably observed. Further details on impact damage in sandwich panels may be found in Davies and Olsson (2004).

3.2 Damage types in impacted fibre reinforced laminates. (Menéndez Álvarez, 1998) © FOI Sweden. Reproduced with permission.

An extensive review of observations of impact damage in laminates was given by Hull and Shi (1993). Impact damage zones may usually be separated into a small local region where damage is induced by contact stresses, and a surrounding region where damage is induced by stresses resulting from flexure and transverse shear forces. For impacts causing large deflections, membrane strains will be significant, particularly close to the impact centre. A local residual deflection is frequently observed, which influences the subsequent compressive behaviour (Melin and Schön, 2001). The sequence of damage formation during static point loading and large mass quasi-static impact has been studied in detail by Kaczmarek and Maison (1994).

Matrix cracks caused by tensile, compressive and shear stresses are normally dispersed within the entire damage region with a concentration close to the impact centre.

Delaminations due to impact are primarily induced by interlaminar shear stresses, which are enhanced by matrix cracks and ply stiffness mismatch. The interaction between matrix cracks, delaminations and fracture modes during impact type loading of thick (span/thickness = 16) 12-ply laminates was studied numerically by Liu (1994). The increase in strain energy release rate due to interior shear cracks was an order of magnitude larger than the influence of surface tensile cracks. The contributions of fracture modes I and III was moderate except for small delaminations. Fractographic evidence of mode II (shear) dominated delamination growth has been provided by Srinivasan *et al*. (1992) and Greenhalgh *et al*. (1996). A typical distribution of delaminations is shown in Fig. 3.3. Fractographic studies of the individual delaminations in laminates have been presented, for example by Levin (1991) and Hull and Shi (1993), for large-mass quasi-static impact and by Kumar and Rai (1993), for small mass dynamic impact.

The current review is primarily based on experience of multidirectional laminates made from conventional unidirectional (UD) tape prepreg. Laminates made from impregnated non-crimp fabrics (NCF) or woven fibre tows will generally have somewhat different damage patterns, although Bibo *et al*. (1998) observed fairly similar damage in laminates made from tape prepreg and from a specific NCF system. In laminates from tape prepreg the delaminations are usually ‘peanut shaped’, extending along the fibres of the lower ply and normally appear between plies of different orientation with an increasing size for increasing misalignment angles. These phenomena have been qualitatively explained by Liu (1988).

A single large delamination frequently appears in the lowermost interface, along matrix tensile cracks induced by bending. The separated sublaminate is, however, usually too thin to significantly influence post-impact strength and buckling induced delamination growth. The region affected by remaining delaminations is usually barrel shaped in thick laminates and slightly conical, expanding towards the non-impacted face in thin laminates (Fig. 3.4) (Olsson *et al*., 2000). The conical damage zone in thin laminates may be explained by the superposition of bending stresses and tensile membrane stresses, which increase the strain energy release rate towards the back face (Suemasu and Majima, 1998).

3.4 Distribution of delaminations for a 48-ply and 16-ply laminate. (Davies and Olsson, 2004). © Royal Aeronautical Society. Reproduced with permission. Compiled from Giugno (1998). © FOI Sweden. Reproduced with permission.

Local compressive and shear failure of fibres has been observed close to the contact area, while local tensile failure of fibres has been observed on the opposite face and in the vicinity of large matrix cracks. More extensive fibre failure normally occurs in the central part of the delaminated region, and appears to be fairly uniformly distributed through the thickness (Sjögren *et al*., 2001). It was noted that fibre failure in thin laminates generally affects more plies and is more extensive than in thick laminates, indicating the importance of membrane stresses in formation of fibre fracture (Fig. 3.5).

3.5 Fibre damage in a 16-ply (left) and 48-ply (right) laminate. (Sjögren *et al*., 2001). © Elsevier. Reproduced with permission.

The fractographic observations discussed so far are based on studies of plain laminates. Fractographic studies of impact damage in skin-stringer carbon fibre reinforced plastic (CFRP) panels have been provided by Greenhalgh *et al*. (1996, 2003) and Wiggenraad *et al*. (1999). The studies included impacts at mid-bay, at the stringer foot edge, and over the stringer centre. Impact damage at some distance from stringers is similar to those of plain laminates. Delaminations close to the stringer foot or support tends to be elongated along the stringer or support. Impact directly above a stringer initially results in local crushing with extensive fibre failure and small delaminations close to the impacted surface, while higher impact energies result in more distributed delaminations, extending along the skin-stringer interface.

## 3.3 Impact response

### 3.3.1 Impact response types

An impact initiates a number of different wave phenomena (Fig. 3.6) over different time scales:

(a) Fast tensile/compressive waves in the plane of the laminate.

(b) Fast surface waves along the laminate surface.

(c) Somewhat slower tensile/compressive waves through the thickness of the laminate.

(d) Relatively slow transient shear and flexural waves within the laminate.

(e) A slow oscillation involving a global quasi-static deflection mode.

The various waves are reflected at boundaries, and sequentially die out due to wave scattering, elastic damping and damping due to damage formation. The through-the-thickness waves Fig. 3.6(c) easily cause damage, as they have large amplitude and act in a direction with low strength, but it is evident that the influence of these waves is fairly local. The strain amplitude *ε _{z}* of the through-the-thickness waves is approximately given by the following expression (Godwin and Davies, 1988):

where *V*_{0} is the impact velocity, *c _{z}* the velocity of through-the-thickness waves, and

*ρ*and

*E*are the density and out-of-plane Young’s modulus of the composite, respectively. When the compressive waves reach the free back surface of a laminate they are reflected as tensile waves, which easily cause local delaminations (‘spalling’) due to the low transverse tensile strength of composites. The laminate will, however, continue to carry load until the compressive strength in the thickness direction is exceeded, which results in penetration. The out-of-plane compressive failure strength of a multidirectional laminate is significantly larger than for common UD specimens, as the fracture planes cut through fibres, while the failure planes of UD specimens only involve matrix failure. Thus, the out-of-plane compressive failure strain of multidirectional laminates is about 3%, while the corresponding value for UD specimens is just above 1% (Collings, 1974; Henriksson, 1990). As a result, the penetration velocity of multidirectional carbon/epoxy laminates is at least 75 m/s.

_{z}If penetration occurs, no more loading is transferred from the impactor to the laminate. If penetration does not occur the impactor will interact with the laminate until its entire kinetic energy has been absorbed.

Penetration during high velocity impact is caused by the through-the-thickness waves which cause a fairly local conical damage zone with a more or less clean hole on the back face. The present chapter does not cover failure due to high-velocity impact. Selected references on high-velocity impact on composites may be found in Abrate (1994, 1998) and Davies and Olsson (2004).

Penetration during low- and medium-velocity impact is caused by tearing of fibres due to large deflections at a late stage in the damage process and will not be considered in the current presentation. Prior to penetration the response and damage depends on the time scale and the dominating wave phenomena at this time scale. It can be shown that the impact time, and hence the response type, is governed by the impactor/plate mass ratio (Olsson, 2000a). For small mass impactors the response is governed by transient waves (types (a) to (d) in Fig. 3.6), while large mass impactors result in the quasi-static response in Fig. 3.6(e). For a central impact on a quasi-isotropic square plate the impact by impactors having a mass less than a quarter of the plate mass will result in small mass impact response, while impactors larger than twice the plate mass result in a quasi-static impact response. A detailed discussion on mass criteria and the effect of plate geometry and orthotropy is provided by Olsson (2000a).

The damage resulting from small mass impact is generally more severe, as only a local region of the plate is affected. This results in a stiffer behaviour, where the damage threshold load is reached earlier and where less energy can be absorbed by elastic deformation. This difference is illustrated by Fig. 3.7, which compares the response and damage from a 10J impact with a 1.5 kg and 10 g impactor (Olsson, 2000a).

3.7 Response and delaminations due to 10J impact by a large and small mass impactor (Davies and Olsson, 2004). © Royal Aeronautical Society. Reproduced with permission. Adapted from Olsson (2000a). © Elsevier. Reproduced with permission. Data and damage pictures from Beks (1996). © FOI Sweden. Reproduced with permission.

### 3.3.2 Large mass impact

Analytical models for impact on plates are useful for understanding damage initiation and growth in composite shell structures, although such models cannot cope with complex geometries or the growth of individual delaminations in a multidirectional laminate.

Impact by an impactor with a comparatively large mass *M* on an elastic plate may be approximated as a single-mass system by setting the plate dynamic mass *M _{p}* =* 0 in the structural model in Fig. 3.8, assuming that the delamination growth load

*F*

_{dn*}is infinite, i.e. that the lower end of the spring

*k*is fixed. The resulting response is quasi-static in the sense that the load-displacement relations are the same as during static loading. In this model, originally proposed by Shivakumar

_{s}*et al*. (1985),

*w*is the impactor displacement,

_{t}*w*the plate deflection at the point of impact,

_{p}*k*represents a nonlinear contact stiffness,

_{α}*k*the bending stiffness,

_{b}*k*the shear stiffness and

_{s}*k*the nonlinear membrane stiffness. All stiffnesses are obtained by dividing the deflection by a corresponding static load at the point of impact. Closed form expressions for the stiffnesses during central impact on circular quasiisotropic plates were presented by Shivakumar

_{m}*et al*. (1985). Corresponding expressions for central impact on rectangular orthotropic laminates have been provided by Olsson (2001). Stiffness for plates of other shapes and for non-central impact on rectangular plates may in some cases be derived from closed form solutions, but in general they have to be derived from numerical solutions, e.g. by finite element analysis.

3.8 Structural model for large mass impact. Adapted from Olsson (2001). © Elsevier. Reproduced with permission.

Intermediate mass impact 1 < *M/M _{p}** < 5 can be modelled by analysing the full nonlinear system with two masses, as described by Shivakumar

*et al*. (1985). When shear and large deflection membrane effects can be neglected, good approximations can be obtained by analysing a linear two mass system, using a properly linearised contact spring, as described in Olsson (1993) and Choi and Lim (2004). In this case the linearised spring must be adjusted to the peak (or average) load during the impact.

In the absence of membrane effects it may be shown that axisymmetric delamination growth in a plate under a concentrated load occurs at a certain threshold load irrespective of the delamination size. Thus, once initiated, delaminations will grow under a constant load if membrane effects are absent. The delamination threshold load was first derived by Davies and Robinson (1992), and subsequently more thoroughly by Suemasu and Majima (1996) using a different approach. A more accessible derivation for an arbitrary number of delaminations, using the original approach by Davies and Robinson (1992), may be found in Olsson *et al*. (2006). In the absence of membrane stresses the most critical interface will be located close to the laminate midplane, but detailed studies show that the delamination threshold load is only weakly dependent on the delamination depth (Olsson, 2001).

For quasi-isotropic laminates the theoretical delamination threshold load has been validated by extensive experimental evidence (e.g. Davies and Robinson 1992; Cartié and Irving 2002). For orthotropic laminates experimental data demonstrate that the delamination threshold load may be obtained by replacing the quasi-isotropic plate stiffness *D* by an effective average plate stiffness *D** (Olsson, 2001):

where . Here *D _{ij}* are elements of the plate stiffness matrix, as given by laminated plate theory. Thus, the delamination threshold load for large mass impact is given by (Olsson, 2001):

where Here G_{IIc} is the interlaminar toughness in mode II, *h* is laminate thickness and an effective (average) flexural modulus of the orthotropic laminate.

The delamination threshold load increases in the presence of membrane effects, as shown by Suemasu and Majima (1998). This effect may be accounted for in an approximate fashion by considering the additional load due to the nonlinear membrane stiffness *k _{m}*, as illustrated in Fig. 3.8. The predicted and experimentally measured delamination threshold load for a range of different layups, plate geometries and boundary conditions for laminates made from carbon/epoxy HTA/6376C prepreg are compared in Fig. 3.9 (Olsson, 2001). It is noted that the expression in Eq. [3.3] represents a lower bound for the delamination threshold load, and that predictions are improved by considering the additional load taken by membrane action.

3.9 Delamination threshold load for various layups and plate geometries (Olsson, 2001). © Elsevier. Reproduced with permission.

It may be concluded that the mode II interlaminar toughness is the single most important material property for increased impact resistance of laminates. It is worth noting that tougher resin systems usually cause a larger increase in the mode I toughness than in the mode II toughness (Reeder and Crews, 1990). Thus, the increase in impact performance of polyether ether ketone (PEEK) laminates has been somewhat lower than expected, as initial material tests were entirely focused on mode I (DCB: double-cantilever beans) testing.

Once delamination has initiated at the most critical interface, additional delaminations will gradually develop in virtually all interfaces of the laminate, which will result in a decreasing load for delamination growth. The effect of the growth of these many peanut-shaped delaminations may be approximated by considering the growth of a smaller number of circular delaminations, having the same total delamination area. As noted by Olsson (2001), the ratio between a typical peanut-shaped delamination and an inscribing circle is about 0.30, based on fractographical studies by Levin (1991). Thus, the effective number *n** of circular delaminations in a laminate with *n* interfaces is given by *n** = 0.3*n*. The load for growth of *n** delaminations is given by (Olsson *et al*., 2006):

The growth of multiple delaminations causes rapidly increasing deflections and membrane effects. The large membrane strains eventually lead to local fibre rupture (fracture) at the point of impact. The load for onset of fibre rupture by membrane effects in a quasi-isotropic laminate was derived by Olsson (2006) and is given by the following expression:

where *E _{r}* and

*v*are the in-plane Young’s modulus and Poisson’s ratio, respectively,

_{r}*ε*

_{1t}is the in-plane tensile failure strain of the laminate and

*R*is the impactor tip radius.

After delamination onset the impact load is controlled by two counteracting effects: a reduction due to an increasing number of delaminations and an increase due to increasing membrane effects. This behaviour may be simulated by using the complete model in Fig. 3.8, i.e. by including the sliding ‘mechanical fuse’ (*F* = *F*_{dn*}) and the membrane stiffness *k _{m}*. The resulting quasi-static prediction and a comparison with an experiment is shown in Fig. 3.10 (Olsson, 2001). In the model a gradual transition was assumed from a single delamination at delamination onset to nine effective delaminations during growth in the 32-ply (30 interfaces) laminate. Due to the quasi-static nature of this impact the load has been plotted versus deflection, rather than versus time. The corresponding time histories, and recorded flexural strains in two laminates are illustrated in Fig. 3.11.

3.10 Predicted and measured load versus deflection during impact. Adapted from Olsson (2001). © Elsevier. Reproduced with permission.

3.11 Measured load and deflection histories during impact (Davies and Olsson, 2004). © Royal Aeronautical Society. Reproduced with permission. Adapted from Olsson (2000b). © FOI Sweden. Reproduced with permission.

After the onset of fibre fracture (rupture), the impact load appears to be truncated and further delamination growth negligible, as illustrated in Fig. 3.12. The fibre rupture energy in this graph is based on combining the structural model in Olsson (2001) with Eq. [3.5], assuming a fibre rupture strain of 1.4%.

3.12 Effect of fibre fracture on delamination size. Data from Olsson (2000b) and Menéndez Álvarez (1998).

### 3.3.3 Small mass impact

Small mass impact response is controlled by local wave propagation in the impacted plate. Hence, it depends on the local contact stiffness, bending stiffness and shear stiffness of the plate but is independent of plate size and boundary conditions. The independence of plate size and geometry is often neglected but can be used to simplify computational models and testing, by only considering a smaller specimen with arbitrary boundary conditions. Due to the local response small mass impacts normally result in very moderate deflections and increased impact energy typically results in penetration rather than in large deflections. For this reason membrane effects can usually be neglected in models of small mass impact.

The structural model in Fig. 3.13 is based on consideration of contact and transient bending and shear waves, while neglecting membrane effects (Olsson, 2003). In this model *M* is the impactor mass and *m* = *ρh* is the plate mass per unit area, where *ρ* is plate density and *h* plate thickness. Furthermore, *w _{i}* is the impactor displacement,

*w*the plate bending deflection at the point of impact,

_{p}*w*the plate shear deflection at the point of impact,

_{s}*k*represents a nonlinear contact stiffness,

_{α}*D** the effective plate bending stiffness and

*S** the effective shear stiffness. Dots represent differentiation with respect to time. The reader is referred to Olsson (2003) for the complete expressions of the various parameters in the model.

3.13 Structural model for small mass impact (Davies and Olsson, 2004). © Royal Aeronautical Society. Reproduced with permission.

The peak load on a plain laminate (*q* = 3/2) during an elastic small mass impact with velocity *V*_{0} may be accurately approximated by the following expression (Olsson, 2003):

where , and

By inspection of Eq. [3.6] it may be concluded that there is a virtually linear relation between the peak load and impact velocity. For thin laminates it can be shown that the influence of the impactor mass is relatively minor, since *F _{b}* <<

*F*,

_{s}*F*.

_{c}The delamination threshold load during small mass impact is very similar to the quasi-static threshold load, but due to inertial effects the threshold load during small mass impact is about 21% larger (Olsson *et al*., 2006):

where *Q*** _{f}* = 12D*/

*h*

^{3}and

*C ≈*1.213.

By equating *F _{peak}* in Eq. [3.6] and

*F*in Eq. [3.7] it is possible to calculate the delamination threshold velocity for a given impactor and plate. Experimental evidence for this approach may be found in Olsson

_{dth}*et al*. (2006) and Olsson (2007). An example of the experimental results in Olsson (2007) is given in Fig. 3.14. Recently the above model was extended to predict delamination growth after delamination onset (Olsson, 2010).

3.14 Comparison between experimental delamination size versus velocity (symbols) and theory (dashed line) (Olsson, 2007). © Japan Society for Composite Materials. Reproduced with permission.

## 3.4 Strength and stability after impact

Impact damage may reduce the strength and stability of composite structures significantly. The effect is particularly large in compression, where reductions of up to 70% of the undamaged strength have been observed. Figure 3.15 illustrates the influence of panel geometry, thickness and boundary conditions on the reduction in compressive failure strain when global panel buckling is prevented. In these tests all panels were tested with anti-buckling plates with a 80 × 80 mm window. It is noted that the reduction in failure strain is smaller for tougher resins, where PEEK represents the toughest resin and 914C the most brittle. It is also noted that thinner laminates generally have a lower compressive strength for a given delamination size. The reason is the more extensive fibre fracture in thin laminates, which is caused by fibre tearing due to more extensive membrane effects during impact on thin laminates, as demonstrated by fractography (Sjögren, 1999).

3.15 Influence of thickness and material on compressive strength after impact (Olsson, 1999). © FOI Sweden. Reproduced with permission.

The reduction in global buckling load is more moderate, and highly dependent on the impact location and delaminated width of the panel. Figure 3.16 illustrates the effects for loading on the short sides of 800 × 200 mm panels with all edges clamped (CCCC), rectangular 239 × 172 mm or 239 × 121 mm plates with the longer edges simply supported (CCSS), and for square 127 × 127 mm plates with the unloaded edges free (CCFF). It is noted that the effect of impact damage on the buckling of the rectangular panels is relatively moderate, except in the presence of penetration and resulting fibre damage or in the case of impact close to clamped unloaded longer edges. The latter case increases the local flexibility at the unloaded edges, which has a strong influence of the buckling load of long panels (Megson, 1972).

3.16 Influence of damage width and panel properties on panel buckling strain (Olsson, 1999). © FOI Sweden. Reproduced with permission.

It has been common practice to quantify damage severity in terms of damage visibility, using the definition of a barely visible damage (BVID), which is assumed to correspond to a certain damage state. Different definitions of BVID are provided by different users/operators but they all have in common that they are expressed in terms of dent depth (0.5–2 mm).

Unfortunately, there is no correlation between dent depth and interior damage (delamination) size, as illustrated in Fig. 3.17. The figure demonstrates that large delaminations can be present without a visible dent, but that a visible dent invariably indicates severe internal damage. Dents are caused by local crushing and local permanent deflections due to inelastic deformations, while delamination growth is caused by more widespread bending and shear. It is obvious that an impact by a blunt impactor may cause fairly large delaminations without visible dent, while a pointed impactor will cause a significant dent with somewhat smaller delaminations. Thus, the visibility of damage depends on boundary conditions and the geometry of the impactor and plate.

3.17 Relation between dent depth and delamination with four different panels and impactors (Olsson, 1999). © FOI Sweden. Reproduced with permission.

Experimental studies of the effect of impact damage on compressive failure of skin-stringer CFRP panels have been provided by Wiggenraad *et al*. (1999), Greenhalgh *et al*. (2003) and Meeks *et al*. (2005). In general there is a complex interaction between local delamination buckling in the damage zone, global skin buckling, buckling-induced delamination growth and eventual skin-stringer detachment. A detailed discussion of these interacting failure mechanisms was provided by Greenhalgh *et al*. (1997).

The effect of impact damage zones on strength and stability after impact is clearly influenced by the following issues: (i) stiffness reduction in the damage zone and how it varies with the applied strain, and (ii) spatial variation of the stiffness within the damage zone. This is schematically illustrated by Fig. 3.18, which shows the interaction between local stiffness reductions and local strain concentrations, which may initiate local failure.

The stiffness of impact damage zones is obviously crucial for understanding their effect on strength and buckling, but experimental data on the constitutive behaviour of impact damage zones is very limited. An early study of the stiffness distribution in impact damage zones was performed by Elber (1983), who studied the spatial variation in tensile stiffness of fibre bundles taken from impact damage zones. A similar study by Sjögren *et al*. (2001) examined both the tensile and compressive stiffness of coupons cut at different distances from the impact centre. Both these studies clearly demonstrated that there is a spatial variation in the stiffness of impact damage zones, but the stiffness was only measured at discrete locations. Furthermore, the use of narrow coupons caused premature fracture in tension due to edge effects, and very premature local buckling in compression, which prevented a description of the complete stress–strain curve to failure. More recently the stiffness of impact damage zones has been examined experimentally by combination of inverse numerical methods and full field displacement measurements based on digital image correlation (DIC) of specimens in the unloaded and loaded states.

The spatial variation of the in-plane tensile stiffness, and its dependency on strain in impact damage zones was studied by Sztefek and Olsson (2008). Figure 3.19 illustrates the variation of tensile stiffness in a 2 mm laminate at two different levels of impact severity, while Fig. 3.20 illustrates the corresponding material nonlinearity in one of these laminates.

3.19 Damage zones and variation of the material properties at two impact energies. Centre: from Sztefek and Olsson (2008). © Elsevier. Reproduced with permission. Left and right: from Sztefek and Olsson (2009). © Elsevier. Reproduced with permission.

3.20 Tensile stress–strain curves at different applied strains *ε*_{0} for three regions of the damage zone in a 4 mm laminate impacted at 14J (Sztefek and Olsson, 2009). © Elsevier. Reproduced with permission.

The compressive membrane stiffness of impact damage zones was studied using a similar approach (Sztefek and Olsson, 2009). Compressive buckling necessitated displacement measurements on both sides of the laminate to separate flexural and membrane deformation. Furthermore, only the apparent average compressive stiffness of the damage zone could be determined, as local buckling in the impact damage zone prevented relevant measurements within the damage zone. Apparent average compressive stress–strain curves for different severities of damage are shown in Fig. 3.21, where figures showing the local buckling of laminate front and back face have been inserted. From these figures it is evident that the softening of the damage zone in compression is associated with local buckling of the entire damage zone, rather than a result of material damage.

3.21 Averaged apparent compressive stress–strain curves of damage zones in 4 mm laminates impacted at various energies (Sztefek and Olsson, 2009). © Elsevier. Reproduced with permission.

An alternative inverse approach, based on measurement of local slopes and the virtual fields method, has been used to determine flexural stiffness variations in impacted laminates (Kim *et al*., 2007).

## 3.5 Computational models

Computational models for prediction of impact damage and its effects on structure have become increasingly popular, mainly due to increased computational power and development of material models capable of modelling damage growth, e.g. delamination growth. The current chapter is aimed at providing understanding of the fundamental mechanisms behind impact damage and its effects. No attempt will be made to cover the extensive and rapidly increasing literature on computational modelling of impact response and damage generation, but a few examples will be given to illustrate recent work in this area. A brief review of methods for prediction of delamination growth during low-speed impact was provided by Elder *et al*. (2004), but further information may be found in more general reviews on methods for modelling delamination growth and damage mechanics. Aymerich *et al*. (2009) recently presented a very detailed comparison of individual delaminations observed by deplying impacted rectangular 12-ply cross-ply laminates and predicted by finite element (FE) simulation with cohesive interface elements. A recent example of the application of damage mechanics for simulation of damage growth during a large mass impact on a stiffened composite panel is the FE simulation by Faggiani and Falzon (2010). The analysis required 96 h using eight parallel CPUs and involved use of damage mechanics in both solid shell elements for modelling intralaminar damage growth and in interface elements for modelling interlaminar damage growth in a 24-ply laminate, where all plies were modelled separately. It is worth noting that real structures often are significantly larger and contain significantly more plies so that the computational costs of sufficiently detailed models often become prohibitive.

The main advantages of computational methods are an ability to cope with complex geometries and the possibility of modelling the entire sequence from impact and damage formation to the subsequent behaviour after impact. Computational times are, however, still considerable (several days for quasistatic impacts). A major problem is that impacts involve very different length scales, i.e. a local area with significant three-dimensional effects and large stress gradients through the thickness, in combination with delamination growth and deflections affecting a region extending much further in the in-plane direction. Thus, simplifications are often necessary, which require experience and judgement to avoid exclusion of important phenomena.

To reduce computational times it is common to use shell elements and/or to model impactors as rigid bodies, but this prevents the ability to correctly consider contact stress fields and indentation which are significant for short impact times and for small span-to-thickness ratios. Contact stresses are also often significant for the initiation and initial growth of impact damage. On the other hand, application of 3D (solid) elements is of little use if each ply is not modelled with at least one element through the thickness, as the mismatch in ply properties is a key factor for interlaminar stresses and delaminations.

Another common simplification in computational models is to replace the laminate plies with fewer but thicker (‘blocked’) plies. Unfortunately, such models will not be applicable on the actual laminate as experimental evidence shows that impacts on laminates with blocked plies result in a lower delamination threshold load and larger delamination widths (Beks, 1996; Olsson, 2000b).

Many computational models have been limited to delamination growth as the sole form of damage, but a detailed numerical study by Liu (1994) has shown that the presence of matrix cracks may increase the delamination growth during impact quite substantially. Furthermore, fibre damage may have a substantial influence on the impact response (Wiggenraad *et al*., 1999) and the delamination growth, as illustrated by Fig. 3.12. Hence, more accurate simulations require that both intralaminar and interlaminar damage growth are included in the model.

When the only aim is approximate prediction of delamination onset, an attractive modelling option is to avoid the need for cohesive elements or application of ply failure criteria by use of a purely elastic model (e.g. with simple shell elements) to predict when the analytical delamination threshold load, Eq. [3.3] or [3.7], is reached. An example of this approach for quasistatic impact problems may be found in Davies *et al*. (2000).

It is safe to say that FE methods are by far the most popular computational method, although other methods, e.g. boundary element and finite difference methods, have been used to analyse impact. Explicit finite element methods are clearly dominating due to their inherent stability and better ability to cope with damage growth and geometrical nonlinearity. The drawback is that the minimum allowable time step in explicit methods is directly related to the shortest propagation time for elastic waves through an element, i.e. to the elastic modulus, density and smallest element dimension. Thus, 3D elements representing the thickness of a ply require extremely small time steps (about 50ns), which often results in prohibitively long computational times for ‘slow’ large mass impacts that usually last several ms. The use of ‘mass scaling’ to reduce analysis times by artificially increasing structural density, which is common in explicit analysis of static problems, is dangerous or impossible in the analysis of impacts, which are inherently dynamic phenomena.

## 3.6 Future trends

Current design practice is still frequently based on the concepts of damage visibility (BVID) and impact energy, but there is a growing awareness that there is no or little relation between dent depth and interior damage size and that equal energy may cause significantly different damage size depending on laminate geometry and impactor velocity. Furthermore, equal damage sizes may result in quite different strength reductions, depending on the degree of fibre damage, etc. This is likely to result in more tailored tests to reflect the actual impact threats of a specific structure, and in the long run in requirements for more appropriate qualification tests.

The advance of computational methods for simulation of damage growth and increased computational power will undoubtedly contribute to a very much increased use of computational methods for virtual testing and design of structures threatened by impact. The interaction between intralaminar cracks and delaminations (interlaminar cracks) necessitates use of computational models which can consider both these phenomena simultaneously, either by solid elements involving 3D damage mechanics or by shell elements with in-plane damage mechanics combined with cohesive elements for delamination growth. The development in this area has just started and further work on robust and efficient methods for simulation of complex damage growth is clearly needed.

In spite of the progress in computational methods, detailed simulation of impact and damage growth will remain a time-consuming business for many years to come. It is hoped that the use of computational methods will be combined with an increasing use of simplified analytical models for initial design and selection of critical impact cases. such an approach would significantly increase the efficiency in design, simplify the selection of critical cases for further numerical analysis and, in certain cases, allow numerical models to be simplified or reduced in size.

So far computational models for generation of impact damage and for the subsequent effect of damage on strength and stability have frequently been separated. In most cases mere geometrical agreement between predicted and observed damage has been used as a measure of modelling success. Future efforts will inevitably be aimed at simulating the entire sequence from impact to strength after impact with a single model. This clearly requires that impact models be capable of predicting not only the geometry of the resulting damage, but also its residual constitutive properties, as measured by Sztefek and Olsson (2008, 2009). While the assumption of a low or zero post-impact stiffness of plies with previously broken fibres may be permissible in tension, such an assumption is clearly not valid in compression.

The damage patterns and post-impact failure mechanisms in textile systems, e.g. non-crimp fabrics (NCF) or 2D and 3D weaves, are significantly different from traditional prepreg systems, as the less well-defined interfaces and the inhomogeneous meso-structure make them less prone to delamination and more prone to distributed matrix cracking. Furthermore, their behaviour is more nonlinear and strongly influenced by fibre waviness. Thus, the introduction of these material systems in structural composites is likely to require renewed studies of impact and revisiting/questioning of several accepted truths for traditional prepreg materials.

## 3.7 Sources of further information and advice

Further information on impacts on composites may be found in a number of books, review papers, journals, conferences, organisations and websites.

A very thorough presentation on the fundamental theory of impact may be found in a book by Goldsmith (1960). The treatment of failure in this book is, however, limited to plasticity in homogeneous materials, which is not directly applicable to composites. The most comprehensive treatment of impact on composites is the book by Abrate (1998). A briefer presentation focused on a few selected models with the character of a handbook was presented by Sierakowski and Newaz (1995). A useful, but hard to access, overview of closed form solutions for impact on composites was provided by Olsson (1993).

Impact on composites and sandwich panels has been exhaustively covered in a number of review papers by Abrate (1991, 1994, 1997). A recent and more selective review, focused on key papers and new contributions was presented by Davies and Olsson (2004). More specialised reviews include a review on modelling of low-velocity impact by Sankar (1996) and a review by Richardson and Wiseheart (1996) on the material aspects.

The only major journal solely devoted to impact is the *International Journal of Impact*, but it covers the area of impact in a very general sense and papers on impact on composites are a relatively minor part of the content. Due to the importance of the topic, papers on impact on composites are frequently published in all the major journals on composite materials, e.g. *Composites Part A/Part B, Composites Science and Technology, Composite Structures* and the *Journal of Composite Materials*. More fundamental papers are often found in the *International Journal of Solids and Structures*.

Impact on composites is a regular topic of special sessions in international conferences, such as the International Conference on Composite Materials (ICCM) and the European Conference on Composite Materials (ECCM). The only specialised conference/workshop on the topic in recent years appears to be ‘Dynamic failure of composites and sandwich structures’ in Touluse on 23–24 June 2011, where a forthcoming book with contributions is planned.

There are a number of organisations working with impact issues. NAFPI (www.nafpi.com) is a US nonprofit association of people and organisations in the aerospace industry working on prevention of foreign object impact damage (FOD) on aircraft. Websites on impact on composites are scarce and usually focused on fairly specific topics. Examples include two websites dedicated to FOD issues: www.nafpi.com run by NAFPI and www.fodnews.com run by the company F.O.D. Control Corporation.

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