Fracture Mechanics Design Approach

Test Piece Manufacture
   Adhesive System Definition
   Loading Conditions for Cyclic Fatigue Testing
   Test Equipment
   Test Deliverables

Test Methods

Part 1   Compliance Calibration Testing
   Pure Mode I
   Pure Mode II and mixed Mode (I + II)
   Part 2   Crack Growth Testing - Ambient Conditions
   Pure Mode I
   Pure Mode II and Mixed-Mode I + II

Part 3 Crack Growth Testing – Non-Ambient Conditions
Conclusions

Fracture Mechanics Design – Example

Fracture Mechanics Design Approach

Introduction

The failure of an adhesive joint can be considered to involve the initiation and propagation of naturally occurring (intrinsic) flaws or defects. These mechanisms can be described by fracture mechanics thus providing a basis for estimating the fracture, fatigue and service life of joints. Fracture mechanics may be considered to be complimentary to stress based approaches, which are useful for initial design. Generally fracture mechanics might be applied once an initial joint geometry has been determined to provide a more detailed design assessment. It may also be used for damage tolerance calculations, which are required by certain design codes particularly for military applications.

Two parameters have been used as the basis to quantify crack growth behaviour:

Stress intensity factor, which considers crack tip stresses

Strain energy release rate, which considers the energy required to create new crack surfaces.

The stress intensity factor was developed for bulk materials. For elastic materials, the stress field around a crack tip is singular. The stress intensity factor K represents the strength of the singularity. The general form of the stress intensity equation for a material is:

(1)

where

(2)

s_o is the applied stress, 2a is the crack length, r and q are the co-ordinates of a point and s_ij are the components of the stress tensor at that point. By combining these equations the stress intensity can be expressed as:

(3)

where Q is a geometry factor.

With the stress intensity method K is used as the basis for assessing failure. For example, for fracture K must exceed the fracture toughness K_c which is a material property representing the critical value for fracture in the material.

In the strain energy release rate method, the parameter considered to govern failure is the strain energy release rate, which is the energy released per unit area of crack growth and is usually denoted as G . For a uniformly loaded joint, the strain energy release rate, can be derived from energy balance considerations as:

(4)

where P is the load, b is the width of the joint, C is the compliance of the joint and a the crack length.

For a crack to grown under monotonic loading, the energy released must exceed the energy required to create the new crack surface (i.e. the strain energy release rate exceeds a critical value denoted as Gc , the fracture energy). Contributions to Gc include the breakage of fundamental bonds in the adhesive and energy dissipating mechanisms around the crack tip, which could include viscoelasticity and plasticity. In general, Gc will depend on loading rate, temperature, thickness of the adhesive layer and type of loading at the crack tip (e.g. the combination of peel and shear).

Although K and G can be related, the stress intensity method is less useful for adhesives as K values are more difficult to calculate and is limited to linear elastic behaviour. With the strain energy release rate method, the nonlinear effects of viscoelasticity and plasticity can be more readily accounted for in the analysis.

In design analysis, G can be used to assess the onset of fracture under extreme loads, the time for the onset of crack growth under static loads (creep failure) and the rate of crack growth under cyclic loads (fatigue failure). It is for the latter that it is most commonly employed.

Crack/adhesive

The failure of adhesive joints depends on the type of loading (e.g. the combination of peel and shear loading). In fracture mechanics three basic ‘modes’ of loading are consider as illustrated in Figure 1.

Mode I – tension/opening Mode II – shearing Mode III - tearing

Figure 1: Basic modes of loading on cracks

Mode I consists of tension across the crack leading to crack opening, Mode II is a shearing action and Mode III a tearing action. G_I , G_II and G_III represent the strain energy release rate in each mode, respectively. In fact, most cracks will experience Mixed-Mode or combinations of loading (most often Mode I and Mode II) which contribute to the total strain energy release rate G_tot . The mixed mode conditions may be described by mixed mode ratios (e.g. G_I /G_tot ).

Mode I is generally considered to be the weakest mode. However, this may not always be the case as the locus of failure within the bondline may be different for Mixed-Mode conditions compared to Mode I.

Next: Fracture Mechanics Design Methodology

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