High strain-rate interfacial behavior of layered metallic composites

Mechanics of Materials 77 (2014) 52–66

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High strain-rate interfacial behavior of layered metallic composites Prasenjit Khanikar 1, M.A. Zikry ⇑ Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA

a r t i c l e

i n f o

Article history: Received 13 February 2014 Received in revised form 12 May 2014 Available online 15 July 2014 Keywords: Interface delamination Dynamic fracture Layered aluminum composite Dislocation Crystal plasticity Finite element method

a b s t r a c t The high strain-rate interfacial behavior of layered aluminum composite has been investigated. A dislocation-density based crystalline plasticity formulation, specialized finiteelement techniques, rational crystallographic orientation relations, and a new fracture methodology for large scale plasticity been used. Two alloy layers, a high strength alloy, aluminum 2195, and an aluminum alloy 2139, with high toughness, were modeled with representative microstructures that included precipitates, dispersed particles, and different grain boundary (GB) distributions. The new fracture methodology, based on an overlapping element method and phantom nodes, along with a fracture criteria specialized for fracture on different cleavage planes is used to model interfacial delamination. Dislocation-density evolution significantly affects the delamination process, and this has a directly related to the strengthening, toughening, and failure of the layered composite. It is also shown that brittle alumina (Al2O3) platelets in the interface region played an important role in interfacial delamination and overall composite behavior. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Layered metallic composites are widely used in applications, which require high strength, toughness, and damage tolerance. The interfaces between constituent layers play an essential role in thermo-mechanical deformation and failure. Interfacial delamination is quite common in layered metallic composite for both quasi-static and dynamic deformations. Delamination in the layered composite can absorb more energy in the deformation process as compared to the energy absorbed by a homogeneous layer of the same thickness comprised of either of the constituents. The extrinsic toughening mechanisms that help to improve the fracture resistance of a layered composite include crack deflection, crack blunting, crack front convolution, stress redistribution, and local plane stress deformation. Interfa⇑ Corresponding author. Tel.: +1 919 515 5237; fax: +1 919 515 7968. 1

E-mail address: [email protected] (M.A. Zikry). Tel.: +1 919 515 5237; fax: +1 919 515 7968.

http://dx.doi.org/10.1016/j.mechmat.2014.07.008 0167-6636/Ó 2014 Elsevier Ltd. All rights reserved.

cial delamination can activate these extrinsic toughening mechanisms (Lesuer et al., 1996). Interface delamination can change the failure mode from shear localization to a mode characterized by energy absorption due to bending and stretching for higher strain rate ballistic impact test (Lesuer et al., 1996). Cepeda-Jiménez et al. have also experimentally shown, for low-strain rate experiments, that the extrinsic toughening mechanisms of interface delamination in a roll-bonded Al-alloy layered composite significantly improves impact toughness by crack renucleation in the next layer (Cepeda-Jiménez et al., 2009). Higher ductility of the layer materials inhibits delamination, whereas the delamination is more likely to happen with a brittle interface (Cepeda-Jiménez et al., 2008). Brittle surface oxide layer, which can have alumina (Al2O3) particles, due to roll-bonding, and these brittle platelets can accelerate delamination by initiating cracks during deformation of layered aluminum composites (Cepeda-Jiménez et al., 2008; Barlow et al., 2004).

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Therefore, in this article, we will investigate the interfacial effects on dynamic behavior of layered aluminum composite for different delamination scenarios. The layered composite configuration to be used here is a rollbonded layered composite of aluminum alloys 2195 and 2139 (Khanikar and Zikry, 2014). In this study, we will use a configuration with the high strength 2195 aluminum alloy on top to investigate how high strain-rate delamination evolves in the layered composite under different conditions. The role of interfacial platelets of alumina on delamination behavior will also be studied. A new fracture approach, which is based on modifying the overlapping element method, will be used with a fracture criteria specialized for different cleavage planes, microstructures, and large scale plasticity. This method surmounts some of the issues associated with other fracture methods, such as XFEM and cohesive fracture. This paper is organized as follows: the microstructurallybased dislocation–density crystalline plasticity formulation and computational approach are presented in Section 2; the microstructural representations are described in Section 3, the computational representation of the fracture surface and the failure criteria are presented in Section 4, the results and discussions are outlined in Section 5 and finally the conclusions are given in Section 6. 2. Constitutive formulation and computational approach

Formulations for the rate-dependent multiple-slip crystalline plasticity, which are coupled to the evolutionary equations for the dislocation densities, were used in this analysis. Detailed presentation can be found in the references (Orsini and Zikry, 2001; Zikry and Kao, 1996; Ashmawi and Zikry, 2002). Only a brief outline of the approach will be presented here. The velocity gradient can be decomposed into a symmetric deformation rate tensor Dij and an antisymmetric spin tensor Wij. Dij and Wij can then be additively decomposed into elastic and plastic components as

Dij ¼ Dij þ Dpij ; W ij ¼

þ

ð1aÞ

W pij :

ð1bÞ

The inelastic parts are defined in terms of the crystallographic slip rates as ðaÞ Dpij ¼ Pij c_ ðaÞ ;

ð2aÞ

ða Þ W pij ¼ xij c_ ðaÞ ;

ð2bÞ ðaÞ

where a is summed over all slip systems, and P ij is the ðaÞ symmetric and xij is the antisymmetric parts of the Schmid tensor in the current configuration. The rate-dependent constitutive description on each slip system can be characterized by a power law relation, for strain rates below a critical value of c_ critical as

#"

sðaÞ jsðaÞ j ða Þ sðrefaÞ sref

#ðm1 1Þ ð3Þ

;

ðaÞ

where c_ ref is the reference shear strain rate, which correðaÞ sponds to a reference shear stress sref , and m is the rate sensitivity parameter. Above the critical strain rate c_ critical , where the phonon drag is assumed to dominate, m is taken as 1. The reference stress saref that was used here is a modification of widely used classical forms (Mughrabi, 1987) that relate the reference stress to a square-root dependence on the dislocation-density qim as ðaÞ ref

s ¼ s

ðaÞ y

qffiffiffiffiffiffiffiffi! n nss X T ðbÞ þ G aab b qðbÞ ; im T 0 b¼1

ð4Þ

ðaÞ

where sy is the static yield stress on slip system a, G is the shear modulus, b(b) is the magnitude of the Burgers vector for slip system b, and the coefficients aab are the slip system interaction coefficients, T is the temperature, T0 is the reference temperature, and n is the thermal softening exponent. The rate of change of temperature due to the high strainrate deformation of the crystal is a function of adiabatic heating. The temperature evolution relation can be obtained from the balance of energy. Assuming adiabatic conditions, the thermal conduction rate can be considered as negligible and the rate of the plastic work can be given by

T_ ¼

2.1. Dislocation-density based crystalline plasticity formulation

W ij

"

c_ ðaÞ ¼ c_ ðrefaÞ

v dev p r D; qC p ij ij

ð5Þ

where v is the fraction of the plastic work converted to v is the deviatoric stress, q is the material density, heat, rde ij and cp is the specific heat of the material. For adiabatic high strain-rate applications, it is assumed that thermal conduction is negligible. 2.2. Dislocation density evolution The crystalline plasticity constitutive formulation has been coupled with dislocation density evolutionary equations to bridge microscopic dislocation activities with macroscopic deformation process. For a given deformed state of the material, it is assumed that the total dislocation density q(a) can be additively decomposed into a mobile and ðaÞ ðaÞ an immobile dislocation density qm and qim as

qðaÞ ¼ qðmaÞ þ qðimaÞ :

ð6Þ

It is assumed that an increment of strain results in a change in the dislocation structure. The balance between generation and annihilation of dislocation densities as a function of strain was thus taken as a basis for the following equations that describe the evolution of mobile and immobile dislocation densities as " ðaÞ dqm g ¼ jc_ ðaÞ j ðasour Þ ðaÞ dt b b

!





#

qffiffiffiffiffiffiffiffi ðaÞ qim g DH g immob  ðminter qðimaÞ ; ðaÞ aÞ ðaÞ exp  kT  ðaÞ qm b b b ð7aÞ

  qffiffiffiffiffiffiffiffi ðaÞ dqim g DH g immob DH ðaÞ ðaÞ g ¼ jc_ ðaÞ j ðminter expð Þþ q expð Þ q ; reco v im im aÞ ðaÞ ðaÞ kT kT dt b b b ð7bÞ

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P. Khanikar, M.A. Zikry / Mechanics of Materials 77 (2014) 52–66

where gsour corresponds to the generation of the mobile dislocation densities, gminter corresponds to the trapping of mobile dislocations by dislocation–dislocation interactions, grecov corresponds to the rearrangement and annihilation of immobile dislocations by recovery and gimmob corresponds to the immobilization of mobile dislocations. The details of the procedure for the determination of these coefficients can be found in reference (Kameda and Zikry, 1998). DH is the enthalpy of activation of plastic deformation, and k is the Boltzmann constant. The g coefficients are assumed the same for all the phases and their values are determined as 2.76  105 (gsource), 0.0127 (gimmob), 5.53 (gminter) and 6.69  105 (grecov) (see Zikry and Kao, 1996; Shanthraj and Zikry, 2011 for a detailed presentation). 2.3. Computational approach The dynamic finite element techniques that were used in this study are based on the formulation of Zikry (1994), and are briefly described here. The total velocity gradient of each element, Lij, and the plastic or elastic velocity gradient, Lpij or Lij , are needed to update the stress state of the element through the Jaumann stress rate aligned with the crystal lattice by the use of the respective deformation rate and spin rate components. An implicit Newmark-b iterative approach using BFGS and one point Gauss quadrature is used to obtain the velocity gradient tensor, Lij, for dynamic analyses. Trapezoidal values of b = 1/4 and c = 1/2 were chosen for unconditional stability. To overcome numerical stiffness issues associated with obtaining the resolved shear stresses and dislocationdensities on each slip-system, a hybrid Runge–Kutta explicit and backward Euler implicit method were used. One point Gauss integration and stiffness based hourglass control were used to control numerical instabilities, which can be triggered by inelastic compressibility. 3. Microstructural representation 3.1. Aluminum Alloy Microstructure Precipitates, dispersed particles, and inclusions can have a dominant effect on the deformation and failure behavior of aluminum alloys. For example, Al-Cu based 2139 aluminum alloy has two nano-sized precipitate 0 phases, X phase (Al2Cu) and h phase (Al2Cu), micron-sized Mn-bearing dispersoids (Al20Cu2Mn3) and larger sized inclusions (Al7Cu2(Fe,Mn)) (Salem et al., 2012). The h0 precipitates, with habit planes of {0 1 0}, have a tetragonal  structure with a space group of i4m2 (Hardy and Silcock, 1955–1956). The X precipitates are also platelet-shaped, and they form on the {1 1 1}Al planes of the matrix (Polmear and Chester, 1989). The commonly accepted structure for the X precipitate is orthorhombic with a space group of Fmmm (Knowles and Stobbs, 1988). In this study, the alternative tetragonal structure, space group I4/ mcm [Garg and Howe, 1991; Ringer and Hono, 2000), was used, which is only a slight perturbation of Fmmm (Wang and Starink, 2005). The Mn-bearing dispersed particles are rod shaped and elongate along the direction of [0 1 0]

(Wang and Starink, 2005). These dispersed particles have an orthorhombic structure with a space group of Cmcm (Mandolfo, 1976). 0 The 2195 alloy has three types of precipitates, a d phase 0 (Al3Li), a T1 phase (Al2CuLi), a h phase (Al2Cu) and one type 0 of dispersed particles, b (Al3Zr) (Polmear, 2006). The 0 spherical d precipitates are an L12 ordered cubic, metasta m (Wang and Starink, ble phase, with a space group of Pm3 2005). These precipitates are fully coherent with the matrix, and the orientation relationship can be described as (1 0 0)d//(1 0 0)Al and [0 0 1]d//[0 0 1]Al. The T1 phase is the primary strengthening precipitates (Chen et al., 1998) and its morphology is similar to the X phase (Al2Cu) of the Al–Cu based 2139 alloy. A commonly accepted structure for T1 precipitates is hexagonal, space group P6/ mmm (Huang and Ardell, 1987a). These precipitates form on {1 1 1} planes of the alloy with mainly brass type textures {1 1 0}h1 2 0i (Chaturvedi and Chen, 2006). The orientation relationship of these precipitates with the matrix is  0 0 i ==h11  0 0Al i (Huang and f0 0 0 1gT1 ==f1 1 1gAl and h1 1 T1 Ardell, 1987b). The deformation mechanism for T1 is different than other precipitates, because it has a hexagonal 0 structure with just three slip systems. The h precipitates (Al2Cu) are same as those of Al–Cu based alloys discussed 0 earlier. The dispersed particles b (Al3Zr) are metastable, L12 ordered cubic with a space group of Pm3m (Prasad et al., 1999). The faceted spherical particles have an orien 0 = == tation relationship of ð1 1 1Þb= ==ð1 1 1ÞAl and ½1 1 b  1 (Prasad et al., 1999). The d0 precipitates nucleate ½0 1 Al 0 around these b dispersed particles (Polmear, 2006). The details of the crystal structures and slip systems of all the above mentioned phases of the two alloys can be found in (Khanikar and Zikry, 2014). 3.2. Rational crystallographic orientation It is known that the precipitate crystals nucleate and grow along rational habit planes in the matrix, which results in an orientation relationship between the slip systems of these precipitates and the matrix. Hence, the rational orientations of the precipitates with respect to the matrix and the global frame of reference have to be determined (Elkhodary et al., 2009; Khanikar and Zikry, 2014). If the precipitates are assumed as non-cubic, the vectors defining the slip-plane normals are not equivalent to their Miller indices, and the normals were obtained by a reciprocal lattice construct. The slip vectors were then mapped from the precipitate space to the matrix space. This can  be obtained by the transformation sequence ½M aCart M Cart X , where ½M Cart  transforms a slip vector in the precipitate X (for e.g. X precipitate) to a vector in a Cartesian frame,  and ½M aCart  transforms the vector from the Cartesian frame to the matrix crystal. The rational orientation relations (Wang and Starink, 2005), ½T aa , are applied to the slip vectors to properly align them with respect to the matrix frame. If the matrix crystal is non-cubic, another transformation ½M Cart a  is needed to transform the slip vectors from the matrix space to the Cartesian space. Random Euler angles were then assigned, through ½T Poly Cart , to orient the crystals with respect to the polycrystalline aggregate axes.

P. Khanikar, M.A. Zikry / Mechanics of Materials 77 (2014) 52–66

Finally, the polycrystalline aggregate axes were then aligned with the finite element frame through the transformation ½T Elem Poly . Thus, the slip directions and slip planes for the precipitates, which were initially in fractional coordinates, were transformed to the element frame as Elem Poly Cart a a Cart ~Elem ~X ~X ½~ nElem X ; sX  ¼ ½T Poly ½T Cart M a ½T a ½M Cart M X ½n ; s :

ð8Þ

4. Computational representation of failure surfaces and failure criterion

55

This approach by Hansbo and Hansbo (2004) has been adapted for large scale plasticity and the complex microstructures associated with the aluminum composite. Fracture approaches, such as XFEM and cohesive fracture as discussed by Ling et al. (2009) and Van der Meer and Sluys (2009), while effective for a broad array of applications, they are suitable for the large scale plasticity and complex microstructures pertaining to this layered aluminum. In the proposed fracture approach, we monitor the stresses on the cleavage planes, and if the fracture criterion is attained, fracture is initiated on those planes. The cleavage fracture of aluminum alloys at high temperature and high strain rate occurs on {1 0 0}a and {1 1 0}a crystallographic planes of the matrix (Deschamps et al., 2002). In this investigation, the cleavage fracture on {1 0 0}a planes were used for the interfacial delamination. The cleavage plane in the current configuration are transformed to global coordinates and updated at every time step due to the lattice rotations (W), which is given by

A method for the representation of the nucleation and growth of failure surfaces using overlapping elements was used for this investigation (Hansbo and Hansbo, 2004). Details of this approach can be found in (Shanthraj and Zikry, 2012). An element in a finite element mesh with area A0 was considered to be crossed by a crack dividing the element domain into two subdomains with areas Ae1 and Ae2 (Fig. 1) The displacement discontinuity due to the crack surface was represented introducing an overlapping element on top of the existing element. The finite-element connectivity of the overlapping elements was defined such that they do not share any nodes and hence they have independent displacement fields. For a 4-node quadrilateral element with reduced integration and hourglass control, the internal nodal force vector of the cracked element is given by Song et al. (2006)

n_ cleav e ¼ W  ncleav e ;

~ ~int ~int f int e ¼ f e1 þ f e2 ;

where rfrac is the critical fracture stress of the material, and tcleave, the maximum of the normal traction components on the cleavage planes, is given by

ð9Þ

~int f int where ~ e1 and f e2 are the internal nodal force vectors of the overlapping elements representing the cracked element, and it is given by

Aðe1=e2Þ ~ f int ðe1=e2Þ ¼ A0

Z

½BT rðe1=e2Þ dAe ;

ð10Þ

ð11Þ

The maximum, over all the {1 0 0}a cleavage planes, of the normal traction components on these planes is, therefore, used as the failure criterion. A crack is assumed to nucleate and propagate along the most favorable cleavage plane when (Morris, 2011; Wang et al. 2008)

t cleav e > rfrac ;

t cleav e ¼ maxhnTcleav e ½rncleav e i:

ð12Þ

ð13Þ

Large scale plasticity can result in instability. When the failure criteria is violated in one element, the elastic energy stored in the element will be released, and the elastic

Fig. 1. Representation of a crack using overlapping elements.

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Fig. 2. Finite element model with a representative Al-alloy microstructure (a) with brittle Al2O3 platelets in the interface region, (b) loading parallel to the interface.

energy releasing rate is then related to plastic work under large plastic deformation. Numerical instability can be encountered, since the resolved shear stresses, slip rates, and dislocation densities can vary widely, due to a sudden loss in stiffness. To address these numerical issues e, a physically-based stress unloading is applied after failure, which is given by

rnþ1 ¼ rn  aN ;

ð14Þ

where N is the number of unloading steps after failure and a is the decay factor. The factor a can be defined as a function of elastic energy (Qe) and plastic work (Qp) and is given by

Qe

a ¼ ebQ p ;

ð15Þ

where b is a constant used to keep a reasonable unloading rate. After unloading the stress to a lower level, overlapping elements are introduced to represent the failure surfaces. For the limiting case of Qe  Qp, which denotes brittle facture, the decay factor a approaches zero, and unloading can be completed in one time step. The three-dimensional cleavage model is implemented in a 2D setting by projecting the 3D crack path onto the two-dimensional plane. Due to the heterogeneities of the

Table 1 Material properties for Al-matrix, precipitates and dispersed particles. Constituents

Young’s modulus (GPa)

Poisson’s ratio

Static yield stress (MPa)

Initial immobile dislocation density (m2)

Initial mobile dislocation density (m2)

Mass density (g/ cm3)

Activation enthalpy/ Boltzmann constant (K)

Al-matrix (2139-alloy) Al-matrix (2195-alloy) h/-precipitates X-precipitates T1-precipitates c/-precipitates Mn-bearing dispersed particles b/-dispersed particles Al2O3

64

0.34

35

1012

1010

2.70

2500

70.4

0.34

38.5

1012

1010

2.70

2500

128 128 345 97 128

0.34 0.34 0.34 0.34 0.34

35 35 38.5 38.5 210

108 108 108 108 108

106 106 106 106 106

4.11 4.36 3.11 2.19 3.60

3100 3100 3100 3100 3100

96

0.34

210

108

106

2.25

3100

2.70

2500

320

0.34

210

12

10

10

10

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57

Fig. 3. Normalized normal stress (normalized by the static yield strength of the matrix) for the perfect delamination case at nominal strains of (a) 0.8%, (b) 1.1% and (c) 2.3%.

microstructure, such as the orientation of precipitates and the hard dispersed particles, multiple cracking can occur.

5. Results and discussion 5.1. Computational model and microstructural representation The two-dimensional finite-element model of the metallic layered composite is assumed to have dimensions of 180  363 lm (Fig. 2(a)). The microstructure with the different precipitates and dispersed particles with elongated grains is also shown in Fig. 2(a). The alumina plate-

lets are added for the special case of brittle interface only. The layered aggregate was deformed in plane strain adiabatic tension with strain-rates that ranged from 1000/s to 50,000/s. In this investigation, we present results for strain rate 50,000/s. Random Euler angles with misorientations less than 10° for each layer were assumed, and the misorientations across the bonded interface were taken as different for different cases. The grain shapes were taken as elongated along the rolling direction, and were generated with Voronoi tessellation. The grain sizes were consistent with experimental sizes on the order of a hundred microns (Lee and Zikry, 2011). A convergent mesh with almost 17,500 elements was used with symmetry

Fig. 4. Normalized normal stress (normalized by the static yield strength of the matrix) along the interface for the planar delamination case.

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Fig. 5. Normalized normal stress (normalized by the static yield strength of the matrix) for the planar delamination case at nominal strains of (a) 0.8%, (b) 1.1%, and (c) 2.3%.

boundary conditions. A total of 36 grains were used for the layered composite, and the roll-bonded interface was chosen as 3 lm thick with material properties based on the rule of mixtures using the properties of the two aluminum alloy layers. The 2195-alloy layer was assumed to have particle vol0 ume fractions of 1% h precipitates, 0.7% T1 precipitates, 0 0 1.2% d precipitates and 0.4% b dispersed particles. The particle volume fractions of the 2139-alloy layer were chosen 0 as 0.7% X precipitates, 1% h precipitates, and 1% Mn-bearing dispersed particles. Table 1 has the material properties for the matrix of each alloy, the precipitates, and the dispersed particles. For the case with an applied strain rate 50,000/s, critical fracture stresses for matrix was chosen

as 1400 MPa, for the precipitates it was 1575 MPa, and for the dispersed particles it was 2800 MPa. These critical fracture stress values are comparable with spall strength values of aluminum alloys (Williams et al. 2012), and fractures stresses can be adjusted for changes in strain-rate hardening and strength (Meyers, 1994). The alumina platelets in the interface region, shown in the figure, can trigger the interface delamination process. To model this mechanism of delamination, 9% volume fraction of alumina platelets are introduced in the interface region. These platelets are taken as brittle in nature and the critical fracture stress is assumed to be 350 MPa. Fig. 2(b) shows a different configuration in which the loading is parallel to the interface. The study of this model

Fig. 6. Normalized shear stress (normalized by the static yield strength of the matrix) plot along the interface for the planar delamination case.

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59

 1Þ½0 1 1 of the matrix Fig. 7. (a) Normalized immobile dislocation density (normalized by saturated dislocation density) on the most active slip system ð1 1 at 2.3% nominal strain, (b) accumulated plastic slip at 2.3% nominal strain, and (c) lattice rotation at 1.1% nominal strain.

was considered, because the orientation of the interface can significantly influence the mode of failure. There were two models considered, one with critical fracture stress of the interface the same as that of the matrix of the two layers and the other with the critical fracture stress of the interface is lower than that of the matrix. In the first case, the stronger interface has a critical fracture stress of

1050 MPa, and in the weaker interface case, the interface has a critical fracture stress of 525 MPa. 5.2. Interfacial delamination To model planar delamination, a pre-existing crack was incorporated into the interface. The pre-existing crack is

Fig. 8. (a) Normalized normal stress (normalized by the static yield strength of the matrix) for the case of interface crack penetration into the top layer, (b) SEM image to show similar crack in an experimental specimen.

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 1Þ½0 1 1 of the matrix for Fig. 9. Normalized immobile dislocation density (normalized by saturated dislocation density) on the most active slip system ð1 1 the case of interface crack penetration into the top layer at nominal strains (a) 1.7%, (b) 2.0%, and (c) 3.5%.

9 lm in length and the crack-length is 0.05 times the width of the specimen (a/W = 0.05). The Euler angles of the interface in this case were taken as (0, 0, 0) to ensure that planar fracture is along the interface. The orientation of the cleavage plane, on which the fracture is modeled to propagate, depends on the Euler angles of the interface. The normal stress contours of the deformed configuration at different stages of deformation are shown in Fig. 3. Fig. 3(a) shows the opening of the pre-existing crack at 0.8% nominal strain before propagation with localized stresses ahead of the crack front. An intermediate stage of delamination at 1.1% nominal strain is shown in the Fig. 3(b). The complete separation of the layers occurred at a nominal strain of

2.3% (Fig. 3(c)). Fig. 4 shows the plot of normalized normal stress, normalized by the matrix static yield stress, along the interface at four different nominal strains. The plot shows the high stresses ahead of the crack front and the decreasing stress distribution away from the crack front. The normal component of the traction on cleavage planes, which is the basis for the fracture criteria (Eq. (13)), depends not only on the normal stresses but also on the shear stress. The shear stress has significant influence on the delamination process. The normalized shear stress contours, normalized by the matrix static yield strength, are shown at different nominal strains in Fig. 5. The opening of the pre-existing crack at a nominal strain of 0.8%

Fig. 10. Comparison of crack extension as a function of time for the two cases, planar delamination and penetration into the top layer.

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61

Fig. 11. Normalized normal stress (normalized by the static yield strength of the matrix) for the case of arrested interface crack at nominal strains (a) 2.0%, (b) 3.4%, and (c) 4.3%.

 1Þ½0 1 1 of the matrix for Fig. 12. Normalized immobile dislocation density (normalized by saturated dislocation density) on the most active slip system ð1 1 the case of arrested interface crack at nominal strains (a) 2.0%, (b) 3.4%, and (c) 4.3%.

(Fig. 5(a)), crack propagation at an intermediate stage, at a nominal strain of 1.1% (Fig. 5(b)), and complete separation at a nominal strain of 2.3% (Fig. 5(c)) are shown. As these figures indicate, localized shear stress developed on either

side of the interface. Fig. 6 shows the normalized shear stress plot along the interface at different nominal strains, and it shows the buildup of the shear stresses, which in combination with the large normal stresses, indicates the

62

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Fig. 13. Normalized normal stress (normalized by the static yield strength of the matrix) for the case of crack nucleation at brittle Al2O3 platelets at nominal strains of (a) 0.8%, (b) 1.1%, and (c) 2.9%.

a high mode of fracture mixity. The evolution of immobile dislocation density on the most active slip system  1Þ½0 1 1, at a nominal strain of 2.3%, is shown in the ð1 1 Fig. 7(a). The values are normalized by saturated dislocation density and hence the immobile dislocation density can be considered to be significant at such a low nominal strains. The accumulated plastic slip is low in this case with highest values in the more ductile bottom layer just below the interface with a maximum value of 0.04 (Fig. 7(b)). The lattice rotation developed in the specimen is also low because of low strain and planar propagation of the crack (Fig. 7(c)).

5.3. Penetration of interfacial cracks into the layers To investigate the penetration of the interface crack into a layer, the Euler angles for the interface are assumed as high angles with values greater than 20°. This interfacial orientation can affect the orientation of the cleavage planes (see Eq. (11)) in such a way that the interface crack penetrates into a layer. The pre-existing crack with the same crack length as the previous case was taken at the interface. Fig. 8(a) shows that the pre-existing crack propagated through a small distance in the interface region, and then penetrated into the top layer. An SEM image of a projectile impacting AA2195–AA2139 layered composite specimen (Fig. 8(b)) shows that this type of crack penetration is possible in layered composite. This SEM image is from a V50 impact test and details are given in (Khanikar et al., 2014). The interface crack was arrested after propagating a small distance, and then the lattice rotation affects the orientation of the cleavage plane. The crack, propagating on a re-orientated cleavage plane, penetrates into the

top layer. Fig. 9 shows the immobile dislocation density evolution in the specimen at different nominal strains. The immobile dislocation density started increasing near the crack front at the crack arrest position (Fig. 9(a)) and gradually saturated the entire bottom layer (Fig. 9(b) and (c)). Even in the top layer, the immobile dislocation density values started rising from near the crack front; however, the values are not as high as in the bottom layer because of the higher strength of the top layer. Fig. 10 shows the comparison of crack extension as a function of time for the planar delamination case and the crack penetration case. The planar delamination case did not have any crack arrest as the (0, 0, 0) Euler angles of the interface, resulted in the cleavage plane remaining normal to the applied load, which facilitates planar crack propagation. The crack layer penetration case did have crack arrest, because of the rotation of the cleavage plane. Once the crack penetrated into the top layer, the propagation did not stop and the crack path direction changed several times. The zigzag nature of the crack path is due to both rotation of the cleavage plane and the switching of cleavage planes.

5.4. Arrested interfacial cracks This model is introduced to study what happens when an interface crack is arrested in the ductile layer. The Euler angles for the interface was taken as high negative angles with values less than 20° to orient the interface crack direction towards the more ductile bottom layer. The pre-existing crack with the same crack length as in the previous cases was introduced at the interface. Fig. 11(a) shows that the pre-existing crack at a nominal strain of 2.2% propagated through a small distance in the interface

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 1Þ½0 1 1 of the matrix, Fig. 14. (a) Normalized immobile dislocation density (normalized by saturated dislocation density) on the most active slip system ð1 1 (b) accumulated plastic slip, (c) lattice rotation, and (d) temperature rise due to adiabatic heating for the case of crack nucleation at brittle Al2O3 platelets at 2.9% nominal strain.

region and then arrested while trying to penetrate into the more ductile bottom layer. The hard Mn-bearing dispersed particles resulted in high local stresses, and this resulted in nucleation of a crack, at approximately at a nominal strain of 3.4% in the weaker matrix near one of the Mn-bearing dispersed particles (Fig. 11(b)). Complete rupture occurred at a nominal strain of 4.3% (Fig. 11(c)). Fig. 12 shows the evolution of immobile dislocation density at three different nominal strains. The immobile dislocation density generated from the arrested crack tip in the interface was more dominant in the more ductile bottom layer while the

evolution in the higher strength top layer was not as significant (Fig. 12(a)). Fig. 12(b) shows the immobile dislocation density at the time of crack nucleation in the bottom layer was quite high with a maximum normalized value attaining saturated values. High dislocation density, which indicates high plastic deformation, can blunt crack fronts and slow crack propagation. Also, higher plastic deformation can lead to a more zigzag nature of the crack. Thus, when an interface crack is arrested, other cracks may nucleate at potential sites of nucleation in the layers, which can grow and lead to complete rupture

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Fig. 15. Normalized normal stress (normalized by the static yield strength of the matrix) for a case with loading direction parallel to the interface, (a) interface with same critical fracture stress as that of the matrix, (b) interface with a smaller critical fracture stress than that of the matrix.

(Fig. 12(c)). The arrested interface crack can influence the nucleation and propagation of the major crack by changing the dislocation density around the crack front. 5.5. Alumina (Al2O3) particles in interface delamination As noted earlier, the brittle alumina platelets in the interface region can trigger the interface delamination process. The surface oxide film is spontaneously formed when the Al-alloy layers are exposed in air. Sometimes this oxide film is removed by surface preparation during the processing of layered aluminum composites. If not removed by surface preparation, these brittle alumina film breaks into small platelets when the composite was processed by roll bonding (Cepeda-Jiménez et al., 2008). The Al-matrix extruded from one layer to the other through the gap between the alumina platelets. The Euler angles of the interface are taken as (0, 0, 0) to achieve a planar fracture along the interface. In this case, there was no pre-existing crack introduced in the model. Fig. 13 shows the sequence of delamination process, which started from the alumina platelets. The two alumina platelets at either end of the interface got fractured at 0.8% nominal strain (Fig. 13(a)) and then the neighboring platelets also failed in the same fashion at a nominal strain of 1.1% (Fig. 13(b)). Finally, the crack propagated and joined to form larger cracks, which almost completely delaminated the two layers at a nominal strain of 2.9% (Fig. 13(c)). Fig. 14(a) shows the evolution of immobile dislocation

density at a nominal strain of 2.9%. The dislocation density generated from the crack fronts and propagated into the layers. Higher dislocation density values occurred in the bottom layer than those of top layer because of the ductility of the bottom layer. The accumulated plastic strain had maximum values of 0.61 near the crack fonts (Fig. 14(b)). High lattice rotation led to geometrical softening near the crack fronts, and hence this affected crack orientations and directions (Fig. 14(c)). The increase in temperature due to adiabatic heating resulted in thermal softening near the crack front (Fig. 14(d)), which coupled with geometrical softening would also soften the layered composite. 5.6. Loading parallel to the interface The loading, in this case, is taken as parallel to the interface. Fig. 15 shows the comparison between normal stresses for an interface with the same critical fracture stress as that of the matrix, and an interface with a critical fracture stress half of that of the matrix. In the case with weaker interface, the interface developed two small cracks, which can be seen near the extreme top and middle of the specimen, and these cracks influences the failure process (Fig. 15(a) and (b)). Both cases are at a nominal strain of 2.2%. For the weaker interface, the crack length is smaller, in comparison with the high strength interface. Hence, interfacial strength has a significant influence on overall behavior of the layered composite. In this case, the weaker interface helps toughening the layered composite.

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6. Conclusions Dynamic interfacial delamination plays an important role in failure and toughening of the layered composites. In this investigation, different delamination scenarios were studied. A pre-existing crack was introduced in the interface to understand the mechanisms of crack propagation along the interface. The planar interfacial delamination case, when a pre-existing crack in the interface delaminates the specimen along the interface, can be faster than the other two cases of interface crack penetration and interface crack arrest. When an interface crack penetrated into a layer, the microstructure can influence the crack path and hence overall time to failure. When an interface crack is arrested in the layer, other cracks nucleate in the regions of high stress adjacent to dispersed particles. In that case, the arrested interface crack can influence the nucleation and propagation of other cracks. The presence of brittle surface oxide platelets can significantly influence the interface delamination process. Cracks nucleate from these brittle platelets and can coalesce to delaminate the whole specimen along the interface. When the loading is parallel to the interface, the configuration with a weaker interface can delay the failure process as compared to the configuration with the stronger interface. All of these interfacial effects and properties can influence on the overall failure or toughening of the composite, and these effects can be tailored to have optimal strength and toughness characteristics. Acknowledgements Support from the US Army Research Office Grant No. W911NF-12-R-0012 is gratefully acknowledged. Discussions and technical cooperation with Brian Gordon of Touchstone are also acknowledged. The authors also acknowledge the use of the Analytical Instrumentation Facility (AIF) at North Carolina State University, which is supported by the State of North Carolina and the National Science Foundation. References Ashmawi, W., Zikry, M.A., 2002. Prediction of grain-boundary interfacial mechanisms in polycrystalline materials. ASME J. Eng. Mater. Technol. 124 (1), 88–96. Barlow, C.Y., Nielsen, P., Hansen, N., 2004. Multilayer roll bonded aluminum foil: processing, microstructure and flow stress. Acta Mater. 52, 3967–3972. Cepeda-Jiménez, C.M., Pozuelo, M., García-Infanta, J.M., Ruano, O.A., Carreño, F., 2008. Influence of the alumina thickness at the interfaces on the fracture mechanisms of aluminum multilayer composites. Mater. Sci. Eng., A 496, 133–142. Cepeda-Jiménez, C.M., Pozuelo, M., García-Infanta, J.M., Ruano, O.A., Carreño, F., 2009. Interface effects on the fracture mechanism of a high-toughness aluminum-composite laminate. Metall. Mater. Trans. A 40A, 69–79. Chaturvedi, M.C., Chen, D.L., 2006. Microstructural characterization and fatigue properties of 2195 Al–Li alloy. Mater. Sci. Forum 519–521, 147–152. Chen, P.S., Kuruvilla, A.K., Malone, T.W., Stanton, W.P., 1998. The effects of artificial aging on the microstructure and fracture toughness of Al– Cu–Li alloy 2195. J. Mater. Eng. Perform. 7 (5), 682–690. Deschamps, A., Péron, S., Bréchet, Y., Ehrström, J.C., Poizat, L., 2002. High temperature, high strain rate embrittlement of Al–Mg–Mn alloy:

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