Elastic-plastic adhesive

Tp=plastic adhesive shear stress in the elastic-plastic adhesive model Ye=elastic adhesive shear strain in the elastic-plastic adhesive model Yp=plastic adhesive shear strain in the elastic-plastic adhesive model. 

When elastic-plastic adhesive behaviour is assumed, the analysis predicts that the adhesive will become plastic first between the butt faces at each end of the step-lap joint. At higher loads, the proportion of the load transferred by the butt faces is reduced as the joint efficiency is increased. 

Pickett A K and Hollaway L (1985), The analysis of elastic-plastic adhesive stress in bonded lap joints in FRP structures . Compos Struct, 4(2), 135-160. 

Pickthall C, Heller M and Rose L R F (1997), Finite element analysis of the double lap joint with an elastic-plastic adhesive , Melbourne, Australia, DSTO Aeronautical and Maritime Research Laboratory, Report no. DSTO-TR-0528. 

Prickett and Hollaway(29) presented both classical and finite-element solutions for elastic-plastic adhesive stress distributions in bonded lap joints. Single, double, and tubular lap configurations having both similar and dissimilar adherends were considered. The results show how the development of adhesive yielding will occur as the joints are loaded to a failure... 

The elastic-plastic adhesive shear mathematical model... 

Despite these great differences in bulk individual mechanical properties, the strength of structural joints (in which the adhesive strains are far from uniform) is far less sensitive to the test temperature than that of short-overlap test coupons (in which the adhesive strains are close to uniform, which is why they are used to generate the stress-strain curves). (This is explained in more detail below, in terms of elastic-plastic adhesive models [Hart-Smith 1973a, 1974]). 

The design and analysis procedures cited in this chapter were developed by the author under three government-sponsored R8dD contracts over a period of years. The first was for NASA Langley during the period 1970-1973 (Hart-Smith 1973b, c, d, e), in which the elastic-plastic adhesive model was introduced and the first of the A4E.. series of Fortran computer codes was... 

R.W. Caipick and M. Salmeron, Scratching the Surface Fundamental Investigations of Tribology with Atomic Force Microscopy,in Chem. Rev. 97 (1997) 1163. (Review relevant technical aspects using AFM for nanotiibology, results on bare interfaces and model lubricant films (SAM s and LB films), aimed at atomic-scale understanding of processes such as friction, the onset of wear, nanometer-scale elasticity, plasticity ind adhesion.)... 

Nanoscratch tests have been used to simulate the effect of third-body particulate wear debris on component surface scratching during use. The load at which the co-efficient of friction or friction force suddenly increases is identified as the critical load, and is used to evaluate scratch resistance and adhesion strength. The depth-sensing nanoindenter, usually equipped with a conical indenter, can elucidate the mode of failure, whether elastic/plastic deformation, cracking, or delamination. 

There has been the question why the TPV materials with ductile thermoplastic matrix display rubber elasticity. Several models have been suggested to answer this question (41 7). Inoue group first analyzed the origin of mbber elasticity in TPVs (43). They constructed a two-dimensional model with four EPDM mbber inclusions in ductile PP matrix and carried out the elastic-plastic analysis on the deformation mechanism of the two-phase system by finite-element method (FEM). The FEM analysis revealed that, even at highly deformed states at which almost the whole matrix has been yielded by the stress concentration, the ligament matrix between mbber inclusions in the stretching direction is locally preserved within an elastic limit and it acts as an in-situ formed adhesive for interconnecting mbber particles. 

Elastic-Plastic Properties of Structural Adhesive Systems... 

An important finding was that instead of an elastic adhesive layer as required by the Gamma method, a plastic adhesive layer could also lead to the same final strength enhancement of about 20% in comparison to conventional glulam. The calculations for the ideal plastic adhesive layer are documented in Donze [6]. The adhesive layer would need to exhibit a yield point at a shear stress below 1 N/mm, but it is very important that it would fail only after a very large shear deformation (Fig. 5). 

The mechanical properties of a new adhesive can be characterized in the lap shear test with small beech specimens connected with the new adhesive. The adhesive manufacturer needed some guidelines as to the results he should aim at. The authors presented him the calculated ideal curves of the shear stress r against the deformation v for both the elastic and the plastic adhesive layers (Fig. 7). The elastic adhesive layer should exhibit a linear relationship for r and v with a given slope. The plastic (or ductile) adhesive should exhibit an initial linear relationship between T and V, but it should yield when the shear stress reaches a value between 0.5 and 1.0 N/mm. ... 

Figure 7. The graph on the left shows the ideal shear stress-deformation curves for small beech specimens (right) with an ideal elastic adhesive coimection or with an ideal plastic adhesive connection. The industrial partner prepared several adhesive layers which exhibited stress-deformation diagrams close to the theoretical requirements. Three of them are shown above 027-2,009-05 and 013-1.

In order that the bipartite beam should attain the higher bending strength as compared to a glulam beam of the same size and wood quality, the theoretical models indicate that the adhesive layers must exhibit a very special load-bearing behaviour. The adhesive manufacturer was able to produce some adhesive layers (like 027-2 in Fig. 7) which attained the requisite load-bearing behaviour for the ideal elastic adhesive layer. However, he was not quite able to fully attain the behaviour required for the ideal plastic adhesive layer. We decided to perform further tests with two selected adhesive layers (009-05 and 13-1 in Fig. 7), which came close to the desired performance needed for the ideal-plastic adhesive layer. There was a need to estimate the performance of bipartite beams with these adhesive connections. A programme based on the Excel solver function was developed to calculate the beam behaviour for these and other adhesive layers as follows. 

In summary, the calculation results for a bipartite beam with an elastic adhesive layer show that, in comparison to a conventional glulam beam, the increased ultimate load-bearing capacity is combined with an increased deformation under service loads. The calculation results for a bipartite beam with a plastic adhesive layer (characterized by non-hnear shear stress-slip behaviour) indicate that it will deform less under service loads, but the increase in ultimate load-bearing capacity will also be slightly smaller than for the bipartite beam with an elastic adhesive layer. 

Adhesive formulations chosen for bending tests. One adhesive (027) satisfied the specifications for an elastic adhesive layer. The other two came close to the requirements for a plastic adhesive layer... 

A total of 45 single lap shear specimens made of beech wood were produced by the adhesive manufacturer as described in Section 3.2. The samples were glued with the five adhesive types used in the delamination test 3 plastic adhesives no. 009, 013 and 014, and 2 elastic adhesives no. 062 and 071. The adhesive layers of the lap shear specimens had the following nominal thicknesses 0.5, 1.0 and 3.0 mm. For each adhesive type and thickness batch, 3 specimens per batch were tested. 

Parameter for overlap Elastic adhesive shear straiu Partial safety factor for the load Partial material safety factor Plastic adhesive shear straiu... 

Figure 5.27 A typical adhesive shear stress distribution in a lap joint according to elastic-plastic model (see reference 5.24, EUROCOMP Handbook).

The rigorous design method is based on generally accepted closed-form models. The adhesive behaviour in the models is assumed to be linearly elastic. Only the formulae used in the calculation of the temporary maximum joint resistance require the complete shear stress—shear strain curve or the elastic—plastic model of the adhesive to be known. As adhesives typically have a non-linear shear behaviour, using only the linear part of the stress—strain curve brings added conservatism to the models with respect to the actual joint resistance. 

Hart-Smith (references 5.25, 5.26, 5.30 and 5.31) has conducted extensive studies of bonded joints using the elastic—plastic model for the adhesive. He has covered the analysis of lap, strap, scarf and step-lap joints. He has modified the load eccentricity induced peel stress approach by using a modified bending stiffness. He has studied the effects of non-uniform adhesive thickness, adhesive non-uniform moisture absorbtion and defects in the bondline. He has also included thermal stresses in his models. 

Strength, unlike elastic modulus, is not even theoretically a readily determinable quantity. Overall elastic-plastic deformation in a structural adhesive might be describable in terms of intermolecular forces and models of viscous flow, but not at the discontinuous moment of fracture. In fact overall behaviour loses sight of the fact that it is normally isolated phenomena that control the magnitude of joint strength and the locus of failure (see Stress distribution mode of failure). The term isolated phenomena refers to voids, cracks, second phase material, and so on, which can act as stress concentrators. Clearly, it would be unwise to suggest that an adhesive bond tester should merely locate and size voids and cracks, as whether or not such a defect is active depends upon where it lies in the working stress pattern of the structure. 

So far all of the analyses discussed or mentioned have assumed linear elasticity of the joint. However, adhesives typically show either plastic or elastic-plastic behavior, depending on the nature of the joint materials. Several investigators have included the nonlinear or time-dependent behavior of the adhesive joint in the stress analysis of single-lap joints. 

Burnett, P.J., Rickerby, D.S., 1988. The scratch adhesion test an elastic-plastic indentation analysis. Thin Solid Films 157, 233—254. 

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