Thermal failure mechanism and failure threshold of SiC particle reinforced metal matrix composites induced by laser beam Y.C. Zhou a, * , S.G. Long a , Y.W. Liu b a Institute of Fundamental Mechanics and Material Engineering, Xiangtan University, Xiangtan, Hunan 411105, China b Department of Engineering Mechanics, Hunan University, Changsha, Hunan 410082, China Received 8 June 2002; received in revised form 1 September 2002 Abstract The failure of particulate-reinforced metal matrix composites (MMCs) induced by laser beam thermal shock is experimentally and theoretically studied. It is found that the initial crack occurs in the notched-tip region, wherein the initial crack is induced by void nucleation, growth and subsequent coalescence in the matrix materials or interface separation. However, crack propagation occurs by fracture of the SiC particle and it is much different from the crack initiation mechanism. The damage threshold and complete failure threshold can be described by a plane of applied mechanical load r max , and laser beam energy density E J . A theoretical model is proposed to explain the damage/failure mechanism and to calculate the damage threshold and complete failure threshold. This model is based on the idea of stress transfer between a reinforced-particle and the matrix, as well as the calculation of the applied mechanical stress intensity factor and local thermal stress intensity factor. In order to check the validity of the theoretical model, the finite element simulations are carried out for the temperature field induced by laser heating, the stress fields induced by the combined laser heating and applied mechanical tensile load. Both the theoretical model and the finite element simu- lation can explain the experimental phenomenon. The theoretical model can predict the damage threshold and failure threshold. The failure of MMCs induced by laser thermal shock and applied mechanical load is non-linear. Ó 2002 Elsevier Ltd. All rights reserved. Keywords: Thermal failure; Particulate-reinforced metal matrix composites; Laser beam; Damage and failure mechanism; Damage and failure threshold 1. Introduction Metal matrix composites (MMCs) are excel- lent candidates for structural components in the aerospace and automotive industries due to their high specific modulus, strength, and thermal stability (Llorca, 2002; Tjong and Ma, 2000). MMCs can be fabricated by standard techniques, * Corresponding author. Tel.: +86-732-8293586; fax: +86- 732-8292468. E-mail addresses: [email protected], yichunzhou@hot- mail.com (Y.C. Zhou). 0167-6636/$ - see front matter Ó 2002 Elsevier Ltd. All rights reserved. doi:10.1016/S0167-6636(02)00322-8 Mechanics of Materials 35 (2003) 1003–1020 www.elsevier.com/locate/mechmat
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Mechanics of Materials 35 (2003) 1003–1020
www.elsevier.com/locate/mechmat
Thermal failure mechanism and failure thresholdof SiC particle reinforced metal matrix composites induced
by laser beam
Y.C. Zhou a,*, S.G. Long a, Y.W. Liu b
a Institute of Fundamental Mechanics and Material Engineering, Xiangtan University, Xiangtan, Hunan 411105, Chinab Department of Engineering Mechanics, Hunan University, Changsha, Hunan 410082, China
Received 8 June 2002; received in revised form 1 September 2002
Abstract
The failure of particulate-reinforced metal matrix composites (MMCs) induced by laser beam thermal shock is
experimentally and theoretically studied. It is found that the initial crack occurs in the notched-tip region, wherein the
initial crack is induced by void nucleation, growth and subsequent coalescence in the matrix materials or interface
separation. However, crack propagation occurs by fracture of the SiC particle and it is much different from the crack
initiation mechanism. The damage threshold and complete failure threshold can be described by a plane of applied
mechanical load rmax, and laser beam energy density EJ. A theoretical model is proposed to explain the damage/failure
mechanism and to calculate the damage threshold and complete failure threshold. This model is based on the idea of
stress transfer between a reinforced-particle and the matrix, as well as the calculation of the applied mechanical stress
intensity factor and local thermal stress intensity factor. In order to check the validity of the theoretical model, the finite
element simulations are carried out for the temperature field induced by laser heating, the stress fields induced by the
combined laser heating and applied mechanical tensile load. Both the theoretical model and the finite element simu-
lation can explain the experimental phenomenon. The theoretical model can predict the damage threshold and failure
threshold. The failure of MMCs induced by laser thermal shock and applied mechanical load is non-linear.
� 2002 Elsevier Ltd. All rights reserved.
Keywords: Thermal failure; Particulate-reinforced metal matrix composites; Laser beam; Damage and failure mechanism; Damage and
Consequently, the stress intensity factor KI, for the
specimen subjected to the coupled loads ðrmax;EJÞ,should be written as,
KI ¼ KTI þ Km
I ð22Þ
Therefore, the stress intensity factors for the
specimen subjected to the coupled loads ðrmax;EJÞcan be used to predict the complete failure
threshold and the results are discussed in the
following section. Here, the contribution of laser
heating to the crack propagating will be dis-cussed. As discussed above, the thermal stress rhh
induced by laser heating is always compressive
within the laser spot region and is tensile around
the laser spot region. The compressive thermal
stress within laser-irradiated region will be re-
sponsible for the close of the crack contrary to
the compressive thermal stress, the tensile stress
around the laser spot region will be responsiblefor the crack opening (Zhou et al., 2001a).
Therefore, the thermal stress, induced by laser
heating, would have a contribution to the stress
intensity factor, as described by Eq. (15). On the
other hand, the laser heating will induce the
temperature rise within laser-irradiated region
and, hence, the material�s fracture toughness will
decrease.
Table 2
Material properties
Parameters Al Matri
Young�s modulus (GPa) 68.3
Yield strength (MPa) 97.0
Poisson�s ratio 0.33
Thermal expansion coefficients (10�6 �C�1) 23.6
Thermal conductivity coefficients (W/cmK) 1.8
Density (g/cm3) 2.7
Specific heat capacity (J/gK) 0.84
Tensile strength (MPa) 278
Percentage elongation (%) 14.5
4.2. Finite element simulation and temperature fields
In order to check the validity of the theoretical
model, the finite element simulations are carried
out for the temperature field induced by laserheating, stress fields induced by the combined laser
heating and applied mechanical tensile load. Fur-
thermore, the maximum stresses in the particle and
matrix are also simulated by considering the
plasticity of the matrix for different couple loads
ðrmax;EJÞ.The ANSYS/LS-DYNA program is used to
simulate the above problem. For the temperaturefield simulation, the material is assumed to be
homogenous and the material parameters of
MMCs are listed in Table 2. The temperature
fields are governed by the following heat conduc-
tivity equation,
qCpo#
ot¼ k
o2#
o2r
�þ 1
ro#
orþ o2#
o2z
�ð23Þ
here z denotes the coordinate in the thickness di-
rection. The heat is assumed to be the absorption
of the laser energy, i.e., k o#=ozjz¼0 ¼ �ð1�R0ÞIðr; tÞ. The temporal shape and spatial dis-tribution of the laser beam are described by
expressions (1) and (2). In the simulation, the
boundary condition is assumed to be adiabatic, i.e.
there is neither and that there is not any other heat
source, nor any other heat loss on the front and
back surface of the specimen. A representative
mesh with 7630 elements and 2510 nodes for the
temperature rise calculation is shown in Fig. 8.In order to study the stress in the particle and at
the interface of MMCs, a two-dimensional unit
cell model is used to represent the whole composite
x SiC Particle MMCs
427 122
– –
0.17 0.30
4.8 20.78
0.42 1.206
3.21 2.82
2.54 1.845
950 600
0.8 6
Fig. 8. A representative mesh for the calculation model of
temperature rise.
1012 Y.C. Zhou et al. / Mechanics of Materials 35 (2003) 1003–1020
and the representative mesh of the unit cell with
742 elements and 780 nodes is shown in Fig. 9. Inthe unit cell, the reinforced particle is assumed to
be a SiC particle with a radius of 10 lm. The
matrix is assumed as the MMCs and its stress–
strain relationship is described by Eq. (11). The
material constants are also listed in Table 2. In the
simulation, the boundary condition is shown in
Fig. 9 with the tensile stress S in the x-directionand the free boundary condition in the y-direction.For a pair of coupled loads (rmax;EJ), the stress
field can be simulated. The stress concerned is the
maximum stress in the particle and interface.
Here, the characteristics of the temperature
fields are given, and the spatial and temporal dis-
tributions of temperature fields are shown in Fig.
10(a) and (b) respectively. Fig. 10(a) shows the
temperature fields on the front surface, i.e. thelaser-irradiated surface for a time of 600 ls with
laser energy density of 40 J/cm2. It is shown that
Fig. 9. A representative mesh for the calculation mo
the spatial distribution of temperature even for a
time of 600 ls is almost the same as the spatial
distribution of laser intensity. The temperature is
almost uniform within the laser-irradiated region
and declines very sharply toward the edge where
the laser spot terminates. Fig. 10(b) shows thehistories of the temperature, both on the front and
on the rear surfaces around the center of the laser-
irradiated region. It is shown that the temperature
gradient in the thickness direction is almost zero
after 1.5 ms. From Fig. 10, it can be concluded
that the temperature gradient is almost zero after
1.5 ms and the temperature conductivity in the r-direction is almost zero even at a time of 600 ls.Therefore, the assumption of Eq. (4) is suitable.
4.3. Damage initiation
The laser beam heating will make the yield
strength Y0 and tensile strengths r�1 of the matrix
degrade at an elevated temperature #. According
to the test results of tensile strength for Al alloy atdifferent temperatures (Wang and Huang, 1996),
the fitting equations of r�1 as a function of tem-
perature is obtained by an approximation of
polynomial function
r�1 ¼ 280F ðT Þ ðMPaÞ ð24Þ
where
F ðT Þ ¼ 1:0� 6:41� 10�3#þ 6:0� 10�5#2
� 2:20� 10�7#3 ð25Þ
del of stress fields near the reinforced particle.
Fig. 10. Temperature fields: (a) two-dimensional distribution of temperature on the laser irradiated surface induced by laser heating
with laser energy density of 40 J/cm2 at time of 600 ls and (b) temperature histories at the center of laser irradiated region both on the
front and rear surface of specimen with laser energy density of 40 J/cm2.
Y.C. Zhou et al. / Mechanics of Materials 35 (2003) 1003–1020 1013
It is assumed that the degradation of rein-
forcement is negligible. As we know from the
above experimental observations, the interfacial
debonding and matrix damage were the main
damage mechanism. It is difficult to measure the
interface fracture toughness of SiC/Al in the
MMCs. However, the experimental results ofShaw et al. (1993) show that the interface fracture
toughness of Al/Al2O3 or Cu/Al2O3 with two
layers should be helpful in evaluating the inter-
face fracture toughness of SiC/Al in the MMCs.
The results given by Shaw et al. (1993) show that
the interface fracture toughness of Al/Al2O3 or
Cu/Al2O3 would increase as the increase of
metal thickness. When the metal thickness is verysmall, for example, 50 lm, the interface fracture
toughness of Al/Al2O3 or Cu/Al2O3 would be
close to the fracture toughness of the ceramic.
Based on this result, it was assumed reasonably
that the interface fracture toughness of SiC/Al in
the MMCs is just the fracture toughness of the
SiC reinforced particle, due to the fact that the
average space distance of particles is about 15 lm.On the other hand, the degradation of the matrix
at elevated temperature will reduce the inter-
face fracture toughness of SiC/Al in the MMCs.
Eventually, it was assumed that the interface
fracture toughness of the SiC/Al in the MMCs
is,
Kc ¼ KSiCF ðT Þ ð26Þ
where KSiC ¼ 3 MPaffiffiffiffim
pis the fracture toughness
of the SiC reinforced particle (Cai and Bao, 1998).
The mechanical stress at the notch-tip was
rmax ¼ arr. Let S ¼ rhhðr; tÞ þ rmax in Eqs. (7) and
(9), for a pair of ðEJ; rmaxÞ, we can easily obtain the
largest stress rp in the particle and the largest in-
terfacial shear stress si. For convenience of anal-ysis, the material parameters are listed in Table 2.
The parameters of the stress–strain relation of the
matrix are taken from the paper of Brockenbrough
and Zok (1995) with N ¼ 0:2, d ¼ 0:1. It should be
pointed out that the combined mechanical and
thermal load for damage initiation is only valid at
the root of the notch, since the assumed stress
concentration due to mechanical load is at theroot. Thus, only particles and interfaces that are
situated at the root are eligible for such a quanti-
fication. It is well known that the interface crack
is a mixed mode crack (Rice, 1988). The stress
intensity factor of the SiC/Al interface crack in
MMCs could be written as
Kin ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiK2