Creep Elastic modulus

A fully automated microscale indentor known as the Nano Indentor is available from Nano Instmments (257—259). Used with the Berkovich diamond indentor, this system has load and displacement resolutions of 0.3 N and 0.16 nm, respectively. Multiple indentations can be made on one specimen with spatial accuracy of better than 200 nm using a computer controlled sample manipulation table. This allows spatial mapping of mechanical properties. Hardness and elastic modulus are typically measured (259,260) but time-dependent phenomena such as creep and adhesive strength can also be monitored. 

Indentation has been used for over 100 years to determine hardness of materials [8J. For a given indenter geometry (e.g. spherical or pyramidal), hardness is determined by the ratio of the applied load to the projected area of contact, which was determined optically after indentation. For low loads and contacts with small dimensionality (e.g. when indenting thin films or composites), a new way to determine the contact size was needed. Depth-sensing nanoindentation [2] was developed to eliminate the need to visualize the indents, and resulted in the added capability of measuring properties like elastic modulus and creep. 

Tackifying resins enhance the adhesion of non-polar elastomers by improving wettability, increasing polarity and altering the viscoelastic properties. Dahlquist [31 ] established the first evidence of the modification of the viscoelastic properties of an elastomer by adding resins, and demonstrated that the performance of pressure-sensitive adhesives was related to the creep compliance. Later, Aubrey and Sherriff [32] demonstrated that a relationship between peel strength and viscoelasticity in natural rubber-low molecular resins blends existed. Class and Chu [33] used the dynamic mechanical measurements to demonstrate that compatible resins with an elastomer produced a decrease in the elastic modulus at room temperature and an increase in the tan <5 peak (which indicated the glass transition temperature of the resin-elastomer blend). Resins which are incompatible with an elastomer caused an increase in the elastic modulus at room temperature and showed two distinct maxima in the tan <5 curve. 

Immediately the load is applied, the specimen elongates corresponding to an instantaneous elastic modulus. This is followed by a relatively fast rate of creep, which gradually decreases to a smaller constant creep rate. Typically this region of constant creep in thermoplastics essentially corresponds to... 

Even in cases where the rigid polymer forms the continuous phase, the elastic modulus is less than that of the pure matrix material. Thus two-phase systems have a greater creep compliance than does the pure rigid phase. Many of these materials craze badly near their yield points. When crazing occurs, the creep rate becomes much greater, and stress relaxes rapidly if the deformation is held constant. 

A and D indicate the two parameters most commonly extracted from a creep curve. A represents the instantaneous elastic compliance and can be used to calculate an elastic modulus. D represents the limiting viscosity, which is related to the reciprocal of the slope. In some cases, parameters from creep testing have been related to molecular mechanisms (Shama and Sherman, 1970 Davis, 1973 deMan et al., 1985). The parameters have also been correlated with hardness and spreadability (Scott-Blair, 1938). 

Fig. 5.5 Effect of changing the elastic modulus ratio and constituent creep stress exponents on the total strain rate of a 1-D composite subjected to tensile creep loading.31 In both (a) and (b), the dashed lines represent the composite behavior, and the thin solid lines the constituent behavior. In the calculations, it was assumed that the creep load was applied instantaneously.

As previously noted, this chapter has been concerned mainly with those models for the creep of ceramic matrix composite materials which feature some novelty that cannot be represented simply by taking models for the linear elastic properties of a composite and, through transformation, turning the model into a linear viscoelastic one. If this were done, the coverage of models would be much more comprehensive since elastic models for composites abound. Instead, it was decided to concentrate mainly on phenomena which cannot be treated in this manner. However, it was necessary to introduce a few models for materials with linear matrices which could have been developed by the transformation route. Otherwise, the discussion of some novel aspects such as fiber brittle failure or the comparison of non-linear materials with linear ones would have been incomprehensible. To summarize those models which could have been introduced by the transformation route, it can be stated that the inverse of the composite linear elastic modulus can be used to represent a linear steady-state creep coefficient when the kinematics are switched from strain to strain rate in the relevant model. 

As expected, magnitudes of instantaneous elastic modulus. Go = (l/./o), and of storage modulus G at 1 rad s (Yoo and Rao, 1996). Also, as noted by Giboreau et al. (1994) for a gel-like modified starch paste, the two parameters were of the same order of magnitude. Further, as can be inferred from data in Table 5-E, the other moduli from creep-compliance data (Gi = 1/Ji, G2 = 1//2) and the Newtonian viscosity increased with increase in °Brix. 

The elastic modulus (E) was calculated directly from the experimental loading-creep-unloading curve (as in Fig. 2.14) according to the procedure of Doemer Nix (1986). 

Elastic modulus Bulk modulus Poisson s ratio Tensile strength Compressive strength Modulus of rupture Fracture toughness Hardness Fatigue Creep... 

Initial moduli at room temperature were obtained with an Instron Model 4206 at a strain rate of 2/min ASTM D638 type V specimens were used. The Instron was also used in the creep experiments, in which deformation under a 1 NPa tensile load was continuously monitored for 10 sec, followed by measurement of the recovered length 48 h after load removal. Strain dependence of the elastic modulus was determined by deforming specimens to successively larger tensile strains and, at each strain level, measuring the stress after relaxation after it had become invariant for 30 min. 

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