T t

Figure 9.6 Sandwich beam loaded in three-point bending and core are t and c, respectively. The faces have a Young's modulus, Ef, and the core has a Young's modulus, Ec, and a shear modulus Gc. The elastic and plastic deflection of a sandwich beam are analysed in Chapter 10. The creep deflection is found from the sum of the bending and shearing deflection rates. Consider the faces first. The power-law creep response of the faces is given by:

where A f and nf are the creep parameters of the face material. Assuming that plane sections remain plane, s = ytc and

1/nf

Assuming also that the moment carried by the faces is much larger than that carried by the core, then

rh/2

lc/2 2b

1/nf yb dy

The bending deflection rate at the center of the beam is then:

The shear deflection rate is calculated from the creep of the core. The power-law creep of the foam core under uniaxial stress is given by:

where ¿0, o0 and nc are the creep parameters of the core material. The core is subjected to both normal and shear loading; in general, for metallic foam cores, both are significant. The creep shear strain rate is calculated using equations (9.6) and (9.7):

da 9^12

<*e = \/ofl + |o-22 + \a\x and that om = o11 /3 gives a =

2 12

Taking the partial derivative with respect to o12 gives:

ah C

doo 1 C (a/3)2 Using equation (9.9) for /(<o) gives:

2 a12

a121 C

2 12

Noting that the normal stress varies through the depth of the beam, in general the shear strain rate has to be integrated over the depth of the beam. The derivative of the shear deflection with respect to x, along the length of the beam, is given by (Allen, 1969):

and the shear deflection rate at the center of the beam is:

Both normal and shear stresses are, in general, significant for metal foam-core sandwich beams. For a given loading, material properties and geometry, the shear and normal stresses can be evaluated and substituted into equation (9.21) to obtain the shear strain rate. This can then be substituted into equation (9.23) to determine the creep deflection rate of the beam. Preliminary data for creep of sandwich beams are well described by equations (9.23) and (9.21).

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