Strengthening and Toughening Mechanism of Metallic System

The metallic properties of strength and hardness are dependent on the mode of plastic deformation. With respect to this, plastic deformation of the metallic system is dependent on the dislocation motion. So, various methods can be implemented to affect the dislocation motion, which proportionally affects the plastic deformation process, and hence, the strength of the metal enriches through strengthening from grain boundaries, solid solution strengthening, strengthening from fine particles, strengthening due to point defects and strain-hardening processes.

Strengthening from Grain Boundary

Fine grains are always preferred over the coarser ones for high strength of the metals. This can be briefly described by the higher strength of bi-crystals as compared with the corresponding single crystals, where with an increase in the misorientation of the grains at the interface leads to an increase in strength. From the plot of yield strength and misorientation, one can obtain the yield strength of single crystal when it is extrapolated to the zero misorientation value. The dependence of strength on grain size can be explained by the Hall-Petch relationship, which is given as follows:

where cr0 is the yield strength of the metal, a, is the friction stress depicting the resistance faced by the dislocation movement due to the crystal lattice, к is the locking parameter that shows the contribution of grain boundaries toward hardening, and D is the grain diameter.

The above equation is found to be equally valid for the resistance to the movement of dislocations by boundaries of twins, plates of martensite, and ferrite-cementite (pearlite) in addition to grain boundaries.

Solid Solution Strengthening

Strengthening of metals is more favored by adding solute atoms to the matrix of the solvent, and this alloying process is used to enhance the strength of pure metals. This process generally occurs in solid solutions, which are of two types: substitutional solid solution and interstitial solid solution. In case of substitutional solid solution, the solute atom has almost the same size as that of the solvent atom, and it occupies the lattice position, whereas in interstitial solid solution, the solute atom sits in the interstitial site due to its comparatively smaller size than the solvent atom. The lattice distortions induced by the solute atoms restrict the dislocation motion, and this leads to an increase in the yield strength of the metal. Strain field around solute atoms impede the interactions with the dislocation and as well their motion, which enhances the strength of metals. Substitutional solute atoms produce spherical distortion, whereas interstitial solute atoms produce non-spherical distortion (maximum strength obtained by non-spherical distortion). The factors that affect the solid solution strengthening are solute atoms’ size, solute atoms’ concentration, stress field symmetry of solute, and solute atoms’ shear modulus.

Strengthening due to Fine Particles

Strengthening by fine particles occurs by two processes: dispersion and precipitating strengthening. In case of dispersion process, the strengthening is obtained by fine dispersed particles in a metal matrix. Dispersion hardened systems are produced by blending and consolidation of second-phase particles (borides, carbide, oxides, and nitrides) with fine powder particles through powder metallurgy route. At higher temperatures, second-phase particles have slight solubility in the matrix; however, the dispersion hardened systems are thermally stable. Dispersion systems lack coherency among the matrix and the second-phase particles. Fine particles exhibit higher resistance toward recrystallization and grain growth. The factors responsible for strengthening from dispersion process are particles’ distribution in matrix, particles’ diameter, and inter-particle spacing.

The precipitation reaction in the solid state can also be regarded as a strengthening mechanism in alloy systems; this is depicted as precipitation hardening or age hardening. In case of precipitation hardening, the alloy system is first solutionized at an elevated temperature and requires higher solubility of the second phase; then, the alloy is quenched as well as aged, which leads to the precipitation of second- phase particles. The precipitation has coherency with the matrix. The presence of second-phase particles creates the tangles of dislocations that get accumulated around the particles; it leads to strain hardening. The strengthening depends on the distribution of second-phase particles in the ductile matrix.

Strengthening due to Point Defects

Point defects are introduced into the metals through various processes such as dislocation interactions leading to jog movements, cooling rapidly from a very high temperature (i.e., close to the melting point), and irradiation with high-energy atomic particles. Rapid cooling from an elevated temperature leads to the accumulation of vacancies, which pin the dislocations identical to the solute atoms and lead to the formation of coarser slip bands. Overall, this effect leads to strengthening of the metallic system. Similar effects are exhibited with vacancy creation by an irradiation process.

Strain Hardening

The process of strengthening and hardening of a metal through plastic deformation is known as cold working/work hardening/strain hardening. The metal deforms plastically due to dislocation movement, and it generates additional dislocations, which lead to more interaction and form the pinned or tangle dislocations. The metal becomes strengthened by impeding the dislocations’ mobility by forming pinned/ tangled dislocations. The strengthening effect obtained by the cold working process (i.e., plastic deformation happens at low temperature, where atoms do not reorder themselves) is superior to solid solution strengthening process. The strain hardening rate is frequently lower for HCP metals than for cubic crystal structure metals. Strain hardening rate of the metal decreases with rise in temperature. The amount of cold work within a metal exhibits significant effect on tensile properties, physical properties, and the overall behavior of the metal. Therefore, an upsurge in amount of cold working has the following effects on the metal:

  • • The elongation and area reduce.
  • • Tensile strength and yield strength increase.
  • • Density decreases to a very small extent.
  • • Electrical conductivity gets reduced to an appreciable extent due to the increase in the number of scattering sites.
  • • Coefficient of thermal expansion increases slightly.
  • • An augmented internal energy of cold worked system increases the chemical reactivity of the metal.

Strain hardening exists because of the obstruction offered to easy glide of a dislocation on a particular slip plane intersected by another one. The causes for strain hardening are dislocation stress fields, produce sessile locks, and interpenetrating slip systems leads to form jogs etc.

Now, the topic is about the toughening mechanisms related to metallic systems such as metals and alloys. Various microstructural features and metallurgical variables control the system toughness. This toughness has a direct relationship with the change in temperature and an indirect one with that of the strain rate. Usually, the increase in strength of a metal leads to a reduction in toughness of the metal. The best method for getting the favorable combination of strength and toughness is the strengthening due to fine particles. Specifically, the best results are obtained for the particles that are small in size (i.e., <100 |im), and they show the best cohesion with the matrix, by preventing the micro-void formation. However, the distribution of these particles should be such that the overlapping of stress fields is prevented, which limits the volume fraction to about 10%. Again, to evade stress concentration, the particles should have round shapes. Presence of inclusions leads to incoherence from the matrix, and hence, they are avoided when high toughness is desirable in the metal. For this weak debonding nature of the inclusions, closely spaced small-sized particles are favorable over the damaging effects of largely spaced particles. Next approach is the grain size effect on toughness; fine particles are preferred over the coarser particles for improving toughness. Anew, any kind of particle accumulation is avoided at the grain boundary, and they are removed by adding small solutes.

Strengthening and Toughening Mechanism of Polymeric Composite System

The strengthening and toughening mechanisms for polymer composite systems are explained in this section. The strengthening mechanisms of the polymer composites are described based on the interface bond. The commonly used strengthening processes are fiber deformation in macroscopic approach and fiber surface as well as transition zone modifications in microscope approach [23]. In advance to this, the nanofillers (carbon nanotubes, graphenes, nanorods, etc.) are used to enhance the strength of the polymer composite systems. The transition zone densification is an effective process due to the weak adhesion between the polymer fibers and cementitious matrix. This process is shown in Figure 3.13a. It is determined from microhardness test that the hardness reaches a minimum in a transition zone with a thickness of

around 50 pm [24]. If it is assumed that the strength scales with this microhardness, then it can be inferred that failure during fiber debonding or pull-out can occur in this weak transition zone. This is the case, strength at point C in the transition zone is lower than adhesion strength at point A. However, if the adhesion strength is lower at point B, then failure can occur directly along the fiber surface. In latter case, this appears to describe most polymeric fibers in a cementitious matrix. For such material system, techniques aimed at strengthening the transition zone, such as by reducing its porosity by using microfillers, tend to be ineffective. However, if the use of microfillers leads to an increase in the contact surface of the transition zone material with the fiber surface, then the adhesion strength may increase, resulting in an increase in the interface bond strength.

Deformed Fibers

The surface area of contact increases with matrix per unit fiber length for most fiber deformation processes. Mechanical interactions between fiber and matrix may occur on the millimeter scale. Hence, in a broader context, the effective bond property must be interpreted. Interfacial bond (i.e., between polymeric fiber and cementitious matrix) can be modified through fiber fibrillation [25,26]. The manufacturing process, controlled by mechanically splitting the extruded polypropylene tape, attains two objectives. It enhances the specific surface area of contact and improves the mechanical bond to the matrix by means of fibrillation. It also improves the fiber modulus by molecular chain alignment. When the fiber is fibrillated, then bond strength improvement can be achieved with a factor of 3 or more, as well as surface treated by chemical additives.

A crimping process, by running a fiber under a loose set of gears, can also be utilized to deform polymeric fibers. It is determined that the pull-out method can significantly change by mechanically crimping a nylon fiber [27]. Significant enhancement of the effective bond strength can be achieved as shown in Figure 3.13b. The fluorocarbon is added so that the fiber can be pulled out instead of failure due to the mechanical locking effect. Another method of improving mechanical anchorage and bonding to a cementitious matrix is through fiber twisting process. It is also reported that a factor of 7 in interfacial bond can be achieved by this method [28].

The toughening mechanisms of polymer composite systems are explained with the help of the following techniques [29]. These methods exhibit the improvement in toughening behavior of epoxy filled with different fillers.

Crack Pinning

This mechanism describes the toughened nature of particulate-filled composites. According to this mechanism, when inhomogeneity is encountered by crack front propagating, it is provisionally arrested by the filler. The degree of bowing between pinning points increases with the extent of loading, which results in the formation of additional fracture surface with enlarged crack length front. It has been observed that the particulate composite fracture energy increases with decreasing particle spacing. Both volume fraction and filler dimensions play a significant role in toughening expansion. The presence of impenetrable fillers in the homogenous matrix leads to significant bowing of crack front, which has its own contribution toward toughening. The appearance of “tails” emanating from the filler particles is a direct evidence of crack pinning mechanism.

Shear Yielding

This mechanism explains the toughened nature of acrylonitrile-butadiene- styrene thermoplastics. It was proposed that the presence of rubber particles initiates matrix shear deformation in diffused form of shear yielding/shear bands formation. The stress concentrations around the embedded filler particles lead to plastic shear yielding in the resin matrix. The filler particles produce a significant triaxial tension in the matrix, which lead to rise in local free volume. It is observed that micro-level shear-bands are initiated through dispersed rubber phase at an angle of 55°-64° to the applied stress direction. However, in composites containing tiny rubber particles, shear deformation stimulated by rubber cavitation is the main contributing factor toward toughening.

Rubber Tear

This mechanism describes the tearing of the rubber particles and deformation in two-phase system. According to this mechanism, the tw'o faces of propagating crack are simply held together by filler particles, and the toughness of such a system is reliant on the energy required to break the particles, together with the fracture of the polymer matrix. The toughness enhancement by filler particle incorporation is assumed to be dependent primarily on the degree of elastic energy stored in the particles during loading of the two-phase system. According to this theory, it is the primary deformation mechanism in the matrix, enriched by the existence of a second phase, which increases toughness. Tearing of rubber particles embedded in epoxy matrix and stretching result in high energy absorption during failure.

Crack Path Deflection

The presence of filler particles leads to the deflection of the primary crack front into several secondary cracks. Local stress intensity of the primary crack is resolved, which changes the crack from principal propagation plane, thereby increasing the area of the crack surface. It is to be noted that this mechanism is relatively less important in rubber-toughened epoxies, but their contribution to thermoplastic- toughened epoxies is rather significant.

Multiple Crazing

This theory states that the increase in toughness could be accredited to the propagation and cessation of crazes through filler particles. A craze seems identical to a crack but is with lower refractive index than its surroundings. It contains fibrils of polymer drawn across, normal to the craze surface, in an interconnecting void network. This mechanism was based on several observed features such as stress whitening ahead of crack tip and the dependence of fracture toughness on particle size. This mechanism has been found to be of particular importance in thermoplastics such as high-impact polystyrene, as confirmed by optical microscopic studies. Crazes are frequently initiated at the site of rubber particles at the equatorial region normal to the applied stress direction and are stabilized on encountering another rubber particle of the craze; their further growth to a large crack is inhibited, and a greater amount of energy can be absorbed by the polymer composites before their complete failure. From the detailed analysis of rubber-modified epoxies, it is determined that the crazing is a dominant toughening mechanism. Donald and Kramer discussed the detailed mechanism of craze initiation, growth, and break down around rubber particles [30]. According to them, an optimum particle size of about 2-5 pm is responsible for maximum toughness, and crazes are rarely mediated from particles smaller than 1 pm.

Cavitation-Shear Yielding

This toughening mechanism is considered the most plausible in recent years. The correlation between toughness and the extent of plastic deformation observed on fracture surfaces has led to a mechanism based on yielding and plastic shear flow of the matrix as the primary source of energy absorption in rubber-modified epoxies. The inclusion of rubber particles leads to enhanced plastic deformation in the matrix. Also, the stress distribution around the rubber particles, particularly in the vicinity of a stressed crack tip, becomes important. Initially, the tri-axial stress around the rubber particles dilates the matrix and subsequently provides the necessary conditions for its cavitation. This process is also responsible for the stress whitening observed in rubber-toughened epoxies. During loading, the increased stress concentrations around rubber particles promote shear yield deformation zones in the polymer matrix. Particle yielding remains localized in the vicinity of the crack tip, as the particles also act as sites of yield terminations. After its initiation, the rubber cavitation would enhance further shear yielding in the matrix. The plastic zone at the crack tip is developed as a result of increase in the blunting of crack tip, which enhances the toughness of the polymer matrix. The high molecular weight and high tensile strength of solid rubber can eliminate premature cavitation, which results in cavitation-free fracture surface of epoxy matrix. Studies have also confirmed that low-molecular-weight carboxyl-terminated butadiene-acrylonitrile rubber is readily cavitated at early stages of loading. It is interesting to note that the fracture toughness of the rubber-modified epoxy is strain rate sensitive. The importance of rubber tearing mechanism is diminished by the process of cavitation, as the failed rubber particles require little or no tearing energy.

3.7.8 Crack Bridging deformation of thermoplastic particles. Broadly, there are two models proposed for crack-bridging mechanism. The crack-bridging model (1) describes the mechanism in rubber-toughened epoxies (i.e., in this crack-bridging model, epoxy toughness is improved by the stretching and tearing of rubber particles during crack development, and this model can be applied to thermoplastic-toughened epoxies with some modifications, as this mechanism is dominant in thermoplastic-toughened epoxies) and (2) describes the mechanism in glass-toughened epoxies (i.e., in this crack bridging model, the impenetrable thermoplastic particles hold the two crack surfaces together and thus restrict the crack propagation).

Physics of Fiber-Reinforced Composite Materials Deformation

In the recent decades, composite materials are preferred in all fields because these materials exhibit superior properties over the conventional materials in terms of their high strength, lightness, and low cost, along with many other advantages. Among these composites, fiber-reinforced composites are especially important because of their high strength-to-weight ratio, and these are fabricated by reinforcing continuous or discontinuous fibers having high strength and modulus than the ductile matrix. For reinforcing purposes, A120, whiskers are proved to give better results, but in most cases, boron or graphite fibers and metal wires are also used. In this material, fibers are the load carriers and matrix is the load transmitter, which maintains gap among the fibers and prevents surface damage of the fibers. The high difference in the elastic moduli of the fibers and the matrix leads to the generation of a very complex stress state whenever the composite is loaded in the direction of fiber alignment. Owing to the load application, two types of stresses are generated: shear stress and tensile stress. Tensile stress emanates because of the applied load, whereas the shear nature exists at the fiber-matrix interface of the polymer composite.

The strength of fiber-reinforced composite is calculated based on the rule of mixtures, and it varies per the direction of load application, such as (a) iso-strain condition and (b) iso-stress condition. The assumptions considered for uniaxial tensile loadings in unidirectional lamina are as follows: fibers are distributed uniformly throughout the matrix; matrix is free from voids; force is applied parallel or normal to fiber direction; elastic nature of fiber as well matrix; and free from residual stresses of fiber and matrix materials. Perfect bonding occurs between the matrix and fibers:

a. When long fibers are reinforced and load is applied longitudinally, as shown in Figure 3.14a. Let us assume a load Pc is applied in the direction of fiber alignment, such that strain for the fiber (g/) and the matrix (£„,) is equal to the total strain for the composite (sc).

For iso-strain condition:

(a) Longitudinal and (b) transverse loadings of a continuous fiber

FIGURE 3.14 (a) Longitudinal and (b) transverse loadings of a continuous fiber.

The total load of the composite can be expressed as follows:

We know that, stress = load/area; therefore, the above equation can be written as follows:

where oy and am are the stresses applied to the fiber and the matrix, respectively, whereas Af and Am are the cross-sectional area of the fiber and the matrix, respectively.

Then, the above equation can be written as follows:

From the volume fractions of fiber (vf=AfIAc) and matrix (v„,=AJAC=(1—Vy)), the above equation can be written as follows:

Or

Divide the above equation with sc on both sides; then, the equation becomes

Or

The equation is known as rule of mixtures.

The fractional load carried through in the longitudinal direction is

Or

The tensile strength in the longitudinal direction of uniaxial continuous fiber composite is

where oy„ is the tensile strength of fiber and

b. When long fibers are reinforced and load is applied transversely to the fiber, as shown in Figure 3.14b. Let us assume that the load applied is Pc, such that the stresses and cross-sectional areas of the matrix and fibers are equal. For iso-stress condition:

The total deformation of composite (ALC) is equal to sum of total deformation of fiber (ДLf) and total deformation of matrix (ДLJ.

Substituting the values of ec = ДLJLC, em = ALm/Lm, and ty= AL/Lf in the above equation, the equation becomes

Divide the above equation on both sides with Lc; here, vf= L/Lc and vra _ LJLC. Then, the above equation is written as follows:

The relation between stress, strain, and modulus is a = e-E. The next step is to apply this relation to the above equation. Then, the equation becomes

where ET is the transverse modulus of the composite. Based on the isostress condition (ac = af= o,). The above equation becomes

The transverse modulus from the above equation is as follows:

The tensile strength in the transverse direction of uniaxial continuous fiber composite is

where cr„„, is the matrix ultimate tensile strength and Ka is the matrix extreme stress concentration.

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