Alternative Mechanical Test Methods

High-performance PE-HD materials are increasingly resistant to SCG and ESC. This entails long test times within development and quality control processes when conventional mechanical test methods are applied. Therefore, time- and cost-effective test methods were sought within the last decades. In this respect, established methods such as the FNCT were modified by introducing new detergents, by applying higher temperatures and by adjusting mechanical stresses to reduce test times. However, this might be questionable since SCG/ESC could not be the dominating mechanisms and the results might not be comparable anymore (section 5.4).

Besides the approach of improving established methods, alternative test methods were developed. Therein, dynamical mechanical loading is typically favored over static tensile loading to reduce test times. Material rankings obtained by dynamic test methods are usually considered to correlate well to traditional static loading methods such as the FNCT [114]. Two alternative SCG test methods mainly applied to PE-HD pipe grades are presented subsequently.

Cracked Round Bar Test

The cracked round bar test (CRB) [114] was developed to determine the SCG behavior of PE-HD and was turned into ISO 18489 recently [115]. CRB specimens are cylindrical bars with dimensions of 80 mm to 100 mm in length and diameters of 14 mm (Fig. 13). A notch with a depth of 1.5 mm is introduced centrally perpendicular to the specimen axis.

Figure 13: Configuration of CRB test specimen according to [115].

CRB is a cyclic tensile test which involves a constant stress range. The circumferential notch in the center of the specimen enables stress-initiated crack propagation. Crack initiation is neglected due to the introduction of a notch prior to the test. The number of cycles until final failure is recorded as a function of the stress range related to the initial crack length and is taken as a measure of SCGR. Due to high constraints and low plastic deformations along the crack tip, the specimen geometry ensures short test times. The cyclic load follows a sinusoidal waveform. The maximum load, the load ratio and the load-cycle frequency are preset parameters. Their values are based on polymer density. CRB is performed in air and addresses SCG. Typically, CRB is performed at room temperature but testing at an elevated temperature is permitted according to ISO 18489. When an elevated

temperature is used, a conditioning time of at least 2 h is indispensable [115]. CRB conditions are selected appropriately to obtain brittle fracture since this is the prerequisite to address SCG.

Kratochvilla, Frank and Pinter evaluated the usability of CRB to describe the SCG behavior of pressure pipes [116] by comparing results to established classical methods such as the notched pipe test (NPT) [117], double-notch creep test (based on FNCT in accordance with [13]) and instrumented Charpy impact test [118, 119]. For PE pipes, a linear correlation of the results of CRB to the afore-mentioned methods was found in terms of the rankings of PE 100 types. These results denote the CRB as an alternative SCG test method with the advantage of lower test times and temperatures used. Moreover, the results of two independent Round Robin tests certify a high reproducibly and reliability to the CRB in terms of material ranking by SCGR [120]. It has to be noted that any influence of fluids (ESC) is unconsidered in CRB. Thus, CRB is capable of providing information on material rankings concerning SCG only. Therefore, it might be predestinated for PE pipe material testing.

Strain Hardening Test

The strain hardening test (SHT) was also developed as a fast and efficient SCG test method for PE- HD pipe materials [121]. It was turned into ISO 18488 [122] most recently.

SHT is a tensile test performed at 80 °C in air. The test specimen is extended along its major axis at a constant speed of 10 mm/min until failure or until its strain reaches 1200%. The elongation is determined by an optical extensometer. A specimen (Fig. 14) of 0.3 mm or 1.0 mm thickness is punched out of a molded sheet after an annealing process. It has a typical tensile specimen shape (ISO 527-2 [123]) with a minimum overall length of 70 mm and a gauge length of 12.5 mm (according to [121] and [122]).

Figure 14: Schematic depiction of SHT specimen according to [122].

For SHT analysis, the draw ratio λd is calculated based on gauge length L and it is expressed as a

dimensionless ratio (Eq. 31): 𝜆_𝑑= ΔL

𝐿0+ 1 (31)

L0 is the initial distance between the gauge marks and ∆L is the increase in specimen length. Above

the natural draw ratio (NDR, 8 < λd < 12), the Neo-Hookean constitutive model (proposed in [122]

and [124]) is used to fit and extrapolate the data of the strain hardening part in the stress-strain curve. Therefrom, the strain hardening modulus <Gp> as the average difference quotient is

calculated (Eq. 32): 〈𝐺_𝑝〉 =_𝑁1∑ 𝜎𝑖+1−𝜎𝑖

𝜆𝑑 𝑖+1−𝜆𝑑 𝑖 𝑁

with σ: true stress and λd: true strain. <Gp> incorporates all N difference quotients between the

onset of the strain hardening part and below the maximum elongation of the stress-strain curve obtained by SHT. <Gp> represents the intrinsic strain hardening and is supposed to be a measure of

the SCGR [3, 121].

This correlation implies that the strain hardening response is determined by the same molecular configurations that govern the SCGR as measured in a classical SCG test such as the FNCT [101]. A possible reason for that can be found in the SCGR being proportional to the magnitude of craze stress which is mainly determined by the effective entanglement density of a polymer. Hence, evaluating the effective entanglement density or the amount of load bearing chains (number of tie molecules) is supposed to be the best measure of the intrinsic SCGR of a polymer. Slender molecular backbones and lower chain stiffness favor high entanglement densities and a high SCGR [3]. Stress- strain data were interpreted thermodynamically first in 1968, when the enthalpic yield processes were separated from the entropic network response of strain hardening [125]. Furthermore, the strain hardening part was considered as a purely entropic response of the entanglement network. Consequently, the strain hardening modulus was considered to be proportional to the node density of a polymer. According to an Eyring thermally activated flow process (section 2.3.3), the resistance to failure of a stretched fibril within a craze is proportional to the square of the number of loaded chains and the effective entanglement density. Because <Gp> reflects the effective density of the polymer

molecular network (𝑣𝑒), the critical strain energy release rate is also proportional to Gp² with

𝐺_𝑝= 𝑣_𝑒𝑅𝑇 = 𝐴Σ_𝑒𝑅𝑇 (33)

Gp: strain hardening modulus in the solid state, R: universal gas constant, T: temperature,

A: constant, Σ𝑒: amount of load bearing chains. Equation 33 represents the basic assumption for the

hypothesis that <Gp> is a valid measure to predict SCGR [3]. For polymers with a high

crystallinity such as PE-HD that have strong secondary interactions [61, 126], the strain hardening response exceeds the (rheological) entanglement density.

For amorphous polymers, a linear scaling of <Gp> with the yield stress was found based on

theoretical considerations [127] and experimental investigations [128]. The dependency of <Gp>

on the yield behavior of a polymer is of major importance, because it implies that the strain hardening contains enthalpic contributions. Therefore, strain hardening scales with the amount of secondary interactions, at least at temperatures far below the glass transition temperature region (Tg) and far below ’-transition for semi-crystalline polymers. The enthalpic effect leads to an

overestimation of <Gp> on the one hand but it is time dependent on the other. This is contrary to

the entropic part. Hence, longer load times result in disappearance of the enthalpic contributions and <Gp> tends towards its entropic value with decreasing strain rate. Since long-term SCGR and long

loading times are to be addressed, strain hardening measurements are supposed to reflect the entropic network contributions and avoid the enthalpic part. Therefore, yield stress and strain rate have to be low [3]. Moreover, the strain hardening becomes independent of strain rate at higher temperatures [129], which indicates an overcome of enthalpic effects. Thus, strain hardening measurements are suggested to be performed at the -transition temperature of PE to eliminate enthalpic contributions [121]. Consequently, a minor stress is necessary to overcome the crystal coherence [3].

SHT can be applied as an alternative approach for material ranking concerning the intrinsic SCGR, which is confirmed by several studies [8, 121, 130, 131]. The simple procedure, the absence of surfactants and notches and the short test times compared to classical SCG test methods are advantageous [101]. However, the influence of environmental fluids causing ESC is unconsidered in SHT.

3. Experimental