Toughening of Epoxies by Thermal Expansion Mismatch
Epoxy resins are ideal engineering adhesives and matrices for fiber composites because of their relatively high stiffness, strength, corrosion resistance, and glass transition temperature. However, they are generally brittle and this has severely restricted their wider application as engineering materials. Hence, various methods have been employed to overcome the tyranny of the Griffith equation in this class of materials. Essentially, these methods are based upon attaining a dispersion of second phase particulates in the epoxy matrix which may be either rubbery' or rigid' in nature, or both.:',4 Substantial enhancement of fracture toughness has been achieved, particularly in the hybrid system.
Various mechanisms of toughening have been proposed for the rubber-modified epoxies?-' Many of these are based on the mechanisms observed in rubber-toughened thermoplastics. Examples of these include: crazing? shear yielding,' shear banding," and rubber stretching and tearing? Each of these theories has inadequacies and cannot explain satisfactorily the microstructure-property-mechanics relations. This note attempts to highlight an alternative toughening mechanism by virtue of the thermal expansion mismatch between the rubbery particles and the epoxy matrix. Its implication on the failure processes is also discussed.
Under suitable conditions, the shrinkage stresses resulting from the thermal expansion mismatch in short fiber composites may contribute to enhance the work of fracture. These stresses if compressive can considerably increase the pullout stress of debonded fibers." The high values of strength and toughness observed in the partially stabilized zirconia (PSZ) ceramics11~'2 have also been attributed to the presence of compressive stresses in the vicinity of the crack tip. These stresses arise from the volumetric expansion of metastable ZrO' particles during the phase transformation. Residual stresses in brittle ceramics and composites may also be harnessed to improve their fracture resi~tance.'~
The differential thermal expansion is a very important parameter in any composite system since it determines the residual stress-strain distributions after fabrication and can have significant effects on the resultant mechanical and fracture properties. When the differential thermal expansion ( A a ) between that of the matrix ( a , ) and that of the filler (a, ) is negative, toughening of the composite may occur. This arises particularly when the filler-matrix interface is strong enough to support the resulting radial tensile stresses on cooling from the fabrication temperature. Under such condition, the surrounding matrix will be subjected to tangential compressive stresses; this will increase the overall strain required to initiate failure. The composite is thus toughened. If however, Aa is positive, induced tangential tensile stresses may weaken and cause embrittlement of the matrix. If the differential is large enough, the failure strain of the matrix may be exceeded and a network of fine microcracks will develop. The magnitude of these radial (a,) and tangential ( q ) stresses may be estimated
where a, T , u, and E are the linear thermal expansion coefficient, temperature, Poisson's ratio, and elastic modulus, respectively. The subscripts refer to the matrix ( m ) and filler ( f ).
In the rubber-modified epoxy system, Aa is negative (aepoxy = 65 X 10-60C-'; arubber > 85 X 10-60C-'). It follows from eq. (lb) that radial tensile stresses of about 6 MPa are induced at the rubber matrix interface on cooling from the curing temperature of 120ยฐC. Since the adhesion between the rubbery particles and the epoxy matrix is very strong,' the interface can support the resulting radial tensile stresses. The rubbery particles will endeavor to strain the matrix in compression in the axial direction. This will invariably increase the fracture resistance of the matrix.