**2.1. Material and mechanical characterization methods**

The resistance of PU elastomers to abrasive and erosive wear is a function of both the testing condition and the properties of the PU. Ductility or softness, yield stress, elasticity, elastoplastic, and viscoelastic behavior are all parameters that can affect the stresses produced within the PU upon impact of erodant particles and, therefore, its wear resistance. To that end, when studying the wear behavior of PU elastomers, identification of the properties with the most significant effect on wear resistance of PU is of great interest. In this section, common experimental techniques to study the mechanical properties of PU elastomers are discussed. Through different testing techniques available for the characterization of PU, focus will be given to testing procedures for determination of parameters that correlate with the abrasive and erosive wear of PU.

### *2.1.1. Hardness testing*

of the erodant particles [21]. In conditions where the erodant particles impact the surface at low angles with respect to the surface (10 to 30°), the cutting mechanism similar to abrasion will be dominant. At low angles, the particle's normal impact force is high enough to enforce the particle for partial penetration, while the tangential force slides the particle along the surface to microcut small pieces from the target surface. As the impact angle increases, the tangential force produced upon impact will not be high enough to cut pieces from the surface. Alternatively, at higher impact angles of 60–90°, ductile targets will mostly experience plastic deformation, and the material removal occurs due to the microforging and extensive deformation of the target surface. The chips formed will detach from the surface at subsequent impacts due to the further accumulation of the residual strains and final detachment of the formed ridges [20]. Since the chipping mechanism of material removal requires higher number of impacts compared to cutting mechanism at oblique impacts, the ductile substrates present a minimal erosion rate at high impact angles. In contrast, the brittle ceramics have the highest erosion rate at normal impact angles, since the particle's normal force is maximum

leading to higher fracture, cracking, and damage of the surface of the brittle substrate.

**2. Wear of polyurethane liners**

134 Aspects of Polyurethanes

and erosive wear of PU.

**2.1. Material and mechanical characterization methods**

In many engineering applications, such as slurry motion of particles in a pipe, the material removal mechanism can be considered as a combination of erosive and abrasive wear. The slurry particles flowing in a pipe may slide onto the pipe bottom surface while being pressed toward the pipe surface by gravity and fluid weight. The motion induced by the flowing fluid and the pushing force can lead to abrasive wear of pipe material. On the other hand, the particles that are freely moving along the fluid stream and suddenly impacting the surface due to the flow turbulences within the pipe represent the erosive wear at low impact angles. Slurry flow in an elbow can be mentioned as another example for conditions in which combined abrasive-erosive wear may occur. Some particles are sliding while being pushed toward the surface, whereas some other particles are freely impacting the surface due to their kinetic energy and inertial forces. Consequently, when studying the wear of protective coatings and liners, the resistance of material versus both abrasive and erosive wear should be evaluated.

The resistance of PU elastomers to abrasive and erosive wear is a function of both the testing condition and the properties of the PU. Ductility or softness, yield stress, elasticity, elastoplastic, and viscoelastic behavior are all parameters that can affect the stresses produced within the PU upon impact of erodant particles and, therefore, its wear resistance. To that end, when studying the wear behavior of PU elastomers, identification of the properties with the most significant effect on wear resistance of PU is of great interest. In this section, common experimental techniques to study the mechanical properties of PU elastomers are discussed. Through different testing techniques available for the characterization of PU, focus will be given to testing procedures for determination of parameters that correlate with the abrasive The hardness testing can be employed as a first-order approximation of ductility of elastomers and plastics [11]. The hardness of elastomers can be measured by a durometer according to the ASTM Standard D2240 testing practice [22]. In this method, the hardness of an elastomer is measured based on the penetration depth of an indenter into the substrate surface. The indentation depth is a function of elastic modulus and viscoelastic behavior of the elastomer [22]. The simplicity of this technique is one of its greatest advantages that allows for quick laboratory testing and in-field evaluations. Although determination of the exact value of elastic modulus is not feasible by this testing technique, the values measured are excellent for comparative evaluation of the elastomer softness. Moreover, monitoring of the indentation depth of the indenter with time can provide data about the viscoelastic response of material and its creep behavior. The hardness testing by durometer according to ASTM Standard D2240 does not provide any information about the elastoplastic behavior.

In a few previous studies [23, 24], it has been shown that the Vickers micro hardness testing that is usually employed for evaluation of the hardness of metals and ceramics [23, 25] can be used as a tool to provide information about the viscoelastic and elastoplastic behavior of polymers. Due to the high elastic deformability of elastomers, the shape of the indent is different from that of metals and a perfect symmetric indentation will not form on the surface. A variation in dwell time of the indenter during the test and also monitoring of the changes in size of the formed indents by time can provide information about the viscoelastic response of elastomers.

### *2.1.2. Tensile and compressive testing*

Data obtained by durometer or Vickers hardness testing do not provide detailed information about the elastomer properties such as the Young's modulus and yield strength. Thorough characterization of PU elastomers can be achieved by testing equipment capable of tensile and/or compression testing at controlled load and displacement. Tensile tests conducted up to failure of the sample can provide information about the elastic modulus, final strength, and elongation at break of the polymer. These are the parameters that can affect the final resistance of a polymeric material to abrasive and erosive wear [21]. The sample size and the applied load and displacement can either be selected from standard testing practices such as ASTM Standard D638 [26] or may be selected similar to the type of loading that occurs in actual erosion or abrasion processes. Tensile testing can also be employed to study the effect of strain rate on the stiffness and strength of materials by testing at different strain rates. This is extremely important when studying the erosive wear of polymeric elastomers since the impact occurs within microseconds at very high strain rates [27]. Beside the tensile testing at different strain rates that can provide information about the viscoelastic response of polymeric materials, relaxation and creep testing can be conducted by this type of testing apparatus either in the form of tensile or compressive stresses. In relaxation tests, the stress relaxation of a material is studied after a sudden displacement at the beginning, while in creep testing, the deformation of the material is monitored upon exposure to a certain stress value [28]. Furthermore, tensile tests can be conducted at controlled temperature to evaluate the effect of temperature on the mechanical response of the studied PU elastomers.

The elastoplastic behavior of PU can be determined by cyclic loading in the form of tensile or compression testing. Cyclic loading-unloading can also provide information about the stress softening (Mullins damage) of elastomers, which is a permanent nonreversible damage to the structure of the material caused by loading [28]. Information about the elastoplastic response of elastomer is essential when studying the wear behavior since in abrasive and erosive wear, the repeated impact of erodant particles produces repeated loading-unloading on the elastomer surface [21].

### *2.1.3. Rebound resilience*

The PU elastomers have better erosion resistance than most metals owing to their softness and high capability for elastic deformation. In fact, the PU elastic deformation enables absorbing the kinetic energy and gradual decelerating of the impacting particles with minimal damage. The kinetic energy absorbed in the form of elastic strain energy will be released later to rebound the erodant particle from the surface. The rebound resilience of PU can be employed as a parameter representing the ability of the elastomer to absorb kinetic energy of the erodant particle upon impact. This property can be measured according to the ASTM Standard D2632 [29]. In this testing practice, a plunger is dropped on the top of the sample surface from certain height. By recoding the rebound height of the plunger, the energy lost during the impact can be calculated. In a fully elastic deformation of the surface upon impact, the plunger would rebound to its initial height. Substrates with higher plastic deformation will restore smaller amounts of plunger energy and the plunger will rebound to a reduced height.
