Relaxations brittle-ductile transitions

Wu, S. (1992). Secondary Relaxation, Brittle-Ductile Transition Temperature, and Chain Structure. J. Appl. Polymer Sci. 46(4), 619-624. 

Several cautions are, however, in order. Polymers are notorious for their time dependent behavior. Slow but persistent relaxation processes can result in glass transition type behavior (under stress) at temperatures well below the commonly quoted dilatometric or DTA glass transition temperature. Under such a condition the polymer is ductile, not brittle. Thus, the question of a brittle-ductile transition arises, a subject which this writer has discussed on occasion. It is then necessary to compare the propensity of a sample to fail by brittle crack propagation versus its tendency to fail (in service) by excessive creep. The use of linear elastic fracture mechanics addresses the first failure mode and not the second. If the brittle-ductile transition is kinetic in origin then at some stress a time always exists at which large strains will develop, provided that brittle failure does not intervene. 

As discussed in Young and Lovell (1991) it is hard to believe that general correlations can be derived between the brittle-ductile transition and molecular relaxations (e.g., Tg data obtained by DSC). Molecular relaxations are detected at low strains, whereas T d is measured at high strains and depends on factors such as the presence of notches, which do not affect molecular relaxations. 

Kackell P., Wenzien B. and Bechstedt R, Influence of Atomic Relaxations on the Structural Properties of SiC Polytypes from Ab-Initio Calculations, Phys. Rev. B50, 17 037 (1994). Kaxiras E. and Duesbery M. S., Free Energies of Generalized Stacking Faults in Si and Implications for the Brittle-Ductile Transition, Phys. Rev. Lett. 70, 3752 (1993). 

Figure 8.9 illustrates the TEM images of the PP/EPR blend with 20 wt% of EPR impacted by different energy (from 5 to 20 J). These images clearly exhibited the microfracture deformation through the formation of craze and voids, which was responsible for the brittle-ductile transition observed during mechanical deformation. The origin of the ductile fracture could be attributed to the relaxation of strain constraint by the microvoids in the craze. 

Reliable revealing micro- and submlcro-plasticity, relaxation and solid-solid phase transitions in brittle and ultra-brittle materials. Some correlations between conductivity (electronic processes) and micro-plasticity, and between the creep rate peaks and brittle-ductile transition could be detected. On this basis, the method for predicting the comparable inclination of materials towards the brittle fracture has been developed. In addition, the kinetic analysis of microplasticity in brittle solids could be performed. 

It is tempting to relate the temperature at which the ductile-brittle transition takes place to either the glass transition or secondary transitions (Section 5.2.6) occurring within the polymer. In some polymers such as natural rubber or polystyrene Tb and Tg occur at approximately the same temperature. Many other polymers are ductile below the glass transition temperature (i.e. Tb < Tg). In this case it is sometimes possible to relate T to the occurrence of secondary low-temperature relaxations. However, more extensive investigations have shown that there is no general correlation between the brittle-ductile transition and molecular relaxations. This may not be too unexpected since these relaxations are detected at low strains whereas Tb is measured at high strains and depends upon factors such as the presence of notches which do not affect molecular relaxations. 

A shortening in relaxation time in the critically strained region makes some materials tough. The shift of relaxation time is attributed to strain-induced dilatation and can reach as much as five decades. Thermal history, on the other hand, dictates the initial state from which this dilatation starts and may be expressed in terms of excess entropy and enthalpy. The excess enthalpy at Tg is measurable by differential scanning calorimetry. Brittle to ductile transition behavior is determined by the strain-induced reduction in relaxation time, the initial amount of excess entropy, and the maximum elastic strain that the material can undergo without fracturing or crazing. 

Eyring s equation may be regarded as a good phenomenological description of yield stress as a function of test parameters (T, e), but it cannot be related to physical processes at the molecular scale. The equation can be used at high e for impact properties and for the prediction of the ductile brittle transition temperature. Eyring s equation can be modified with two sets of parameters if two relaxations are involved in the range of temperatures and strain rates (Bauwens-Crowet et al., 1972). 

The first secondary transition below Tg, the so called fj-relaxation, is practically important. This became evident after Struik s (1978) finding that polymers are brittle below Tp and establish creep and ductile fracture between Tp and Tg. The p-relaxation is characteristic for each individual polymer, since it is connected with the start of free movements of special short sections of the polymer chain. In view of more recent data of Tp Boyer s relation, Eq. (6.29), is very approximate and fails completely for amorphous polymers with high Tg s (e.g. aromatic polycarbonates and polysulphones). Some rules of thumb may be given for a closer approximation. 

Recently Moore and Petrie (5) have demonstrated that control of sample thermal history can result in transition from ductile to brittle behavior for polyethylene terephthalate. This transition in behavior was related to volume relaxation of the glassy state. 

The effects of morphology (i.e., crystallization rate) (6,7, 8) on the mechanical properties of semicrystalline polymers has been studied without observation of a transition from ductile to brittle failure behavior in unoriented samples of similar crystallinity. Often variations in ductlity are observed as spherulite size is varied, but this is normally confounded with sizable changes in percent crystallinity. This report demonstrates that a semicrystalline polymer, poly(hexamethylene sebacate) (HMS) may exhibit either ductile or brittle behavior dependent upon thermal history in a manner not directly related to volume relaxation or percent crystallinity. 

In conclusion, the deformation behavior of poly(hexamethylene sebacate), HMS, can be altered from ductile to brittle by variation of crystallization conditions without significant variation of percent crystallinity. Banded and nonbanded spherulitic morphology samples crystallized at 52°C and 60°C fail at a strain of 0.01 in./in. whereas ice-water-quenched HMS does not fail at a strain of 1.40 in./in. The change in deformation behavior is attributed primarily to an increased population of tie molecules and/or tie fibrils with decreasing crystallization temperature which is related to variation of lamellar and spherulitic dimensions. This ductile-brittle transformation is not caused by volume or enthalpy relaxation as reported for glassy amorphous polymers. Nor is a series of molecular weights, temperatures, strain rates, etc. required to observe this transition. Also, the quenched HMS is transformed from the normal creamy white opaque appearance of HMS to a translucent appearance after deformation. 

The observed peak in fracture energy is similar to that reported in the literature for many polymers [28-32]. In these reported cases, the observed peak has often been suggested to be due to the molecular relaxation process. The brittle behavior for temperatures below the peak implies that the molecular motions are limited. Above the transition temperature, the ductile behavior offracture indicates that movements of certain segments or regions of macromolecules... 

The secondary relaxations are very important because they are often associated with the onset of ductility ( toughness ) in polymers with increasing temperature under mechanical deformation. The semiquantitative relation between the "ductile-brittle transition temperature" and Tp has stimulated much experimental and theoretical work on secondary relaxations. 

Crystalline polymers exhibit more mechanical relaxations than amorphous polymers. It is not an overstatement to remark that the greater number of mechanical relaxations in crystalline polymers is the cause of the substantial difference in properties between crystalline and amorphous polymers (4.N.4). For example in linear (LPE) and branched (BPE) polyethylene at temperatures above — 200 "C, there is a sequence of relaxations (see Fig. 4.12). In branched PE the processes are y-relaxation at — 120 C, -relaxation at — lO C, and a-relaxation at 70 C. The presence of a relaxation is detected most easily by the peak in A this is one reason why this parameter is of value. The relaxation observed in creep in linear PE at room temperature and above (shown in Fig. 4.4) is the a-process. The torsion pendulum is a useful tool for yielding quickly a description of temperature regions where creep or stress-relaxation processes are to be expected. In addition, the relaxation temperatures often mark transitions in ductility the polymer becomes increasingly brittle as it is eooled. 

The transition from ductile to brittle behavior is related to the relaxation enthalpy of the free volume. Figure 5.200 shows the increase in relaxation enthalpy with increasing exposure temperature and longer exposure times yield strain decreases simultaneously [773]. 

---