In order to understand glass design, some knowledge about glass testing procedures is indispensable. Some of the most commonly used laboratory testing are, therefore, briefly outlined hereunder.
3.5.1 Testing procedures for crack velocity parameters
The following testing procedures are widely used to determine crack velocity parameters (see Section 3.2.1):
Direct measurement of the growth of large through-thickness cracks.
Particularly before measurements on indentation cracks (see below) became popular, this experimental approach was used to determine crack velocity parameters. The growth of a large through-thickness crack is directly measured as a function of the stress intensity factor, for instance optically or using sound waves. On one hand, this is a direct and relatively precise approach. On the other hand however, the behaviour of such large through-thickness cracks is not necessarily representative of the behaviour of the relatively small surface flaws that are relevant for structural design of glass elements. While Richter[284] (cf. above) could only measure crack velocities in the range of 10−5mm/s ≤ v ≤ 10−2mm/s, which is clearly above the range that is relevant for structural glass
design18, modern technologies such as atomic force microscopy allow measurements within a wider range of 10−9mm/s ≤ v ≤ 1 mm/s [246].
Direct or indirect measurement of the growth of indentation flaws.
Since indentation flaws are relatively small surface flaws, they are more representative of the flaws governing failure of structural glass elements than long through-surface cracks. The advantage of indentation flaws over ‘natural’ surface flaws is that their fracture mechanics characteristics are well known, which is crucial if accurate crack velocity
parameters are to be obtained. The growth of indentation flaws may either be observed directly or derived from ambient strength data.19
3.5.2 Testing procedures for strength data
Static long-term tests
Static long-term tests with constant stress, also known as ‘static fatigue tests’, are usually performed using a four point bending test setup. The testing procedure consists in applying a constant load and measuring the time to failure. The main advantage of such tests is their similarity with in-service conditions of structural glass elements that carry mainly dead loads. The disadvantage is that such tests are extremely time-consuming. If a specimen’s surface condition or the stress corrosion behaviour differs only slightly from the assumptions used to design the test, the specimen may only fail after several years or not at all.
Dynamic fatigue tests
The term ‘dynamic fatigue test’ is a generic term used for constant load rate testing, for constant stress rate testing, and for testing with cyclic loading. It is mostly performed using four point bending (P4B) or coaxial double ring (CDR) test setups (also known as concentric ring-on-ring tests). Figure 3.9 shows a schematic representation of the two test setups. load glass specimen load loading ring reaction ring glass specimen reaction reaction reaction
Figure 3.9: Schematic representation of coaxial double ring (left) and four point bending (right) test setups.
In 4PB tests, the specimen is exposed to an approximately uniaxial stress field (σ16= 0,
σ2= 0). In CDR tests, an equibiaxial stress field (σ1= σ2) is obtained.20
Both test setups are simple and provide short times to failure even for specimens with small surface defects (e. g. as-received glass). The failure stress is a function of the stress rate. When plotting this relationship on logarithmic scales, a line with a slope of 1/(n + 1) is obtained. If v0is constant, this allows for the determination of the crack velocity parameter n from tests at different stress rates.
In Europe, the testing procedure that is mostly used to obtain glass strength data is the coaxial double ring test. It is standardized in EN 1288-1:2000[109] (fundamentals),
19For details on the procedure, see e. g.[177, 298, 301, 302].
20For detailed information on the CDR testing procedure, the interested reader should refer to seminal work
EN 1288-2:2000[110]21(R400 test setup) and EN 1288-5:2000[112] (R45 and R30 test setups). Details on the different setups are given in Table 3.10. Another common procedure, the four point bending test, is standardized in EN 1288-3:2000[111]. In all these tests, the stress rate to be used is 2± 0.4 MPa/s.
Table 3.10: Coaxial double ring test geometries in European standards.
Designation Standard Loading Reaction Tested Specimen
ring radius ring radius area∗ edge length
(mm) (mm) (mm2) (mm)
EN CDR R45 EN 1288-5[112] 9 45 254 100(±2)
EN CDR R400 EN 1288-2[110] 300± 1 400± 1 240 000† 1 000(±4) ∗This is the surface area in uniform, equibiaxial tension= the area inside the loading ring (exception, see†). †This is the value from the code. It does not correspond to the area within the load ring (282 743 mm2).
Testing is mostly done on as-received glass specimens or specimens with artificially induced homogeneous surface damage. The data obtained represents a combination of the specimen’s surface condition and the crack growth behaviour during the tests. Statistical analysis of the test results is generally done by fitting a two-parameter Weibull distribution[331, 332] to the experimental failure stress data:
Pf(σf,A) = 1 − exp − σ f,A θA β (3.65)
Pf(σf,A) is the cumulative probability of failure and σf,Ais the failure stress of specimens of which the surface area A is exposed to tensile stress.θAis the scale parameter (depends on
A) andβ the shape parameter of the Weibull distribution. Various methods for parameter estimation exist. The procedure standardized in EN 12603:2002[102] was often used in the past.22It is based on point estimates and the median-rank based empirical failure
probability given in Equation (C.6). For details on this approach as well as on alternative methods, see Section C.3.
For a general introduction to Weibull statistics, the interested reader should refer to a statistics book, e. g.[25, 253].
Tests for the glass failure prediction model
The underlying model of the US and Canadian Standards, the so-called glass failure prediction model (GFPM), does not use the above-mentioned testing procedures. The two interdependent surface flaw parametersme and ˜k are determined by loading rectangular glass plates with uniform lateral load. The visually determined failure origin, the stress history at the failure origin and a rather complex iterative procedure are used to find the parameters (see Section 4.4.1). Only one crack velocity parameter, n= 16, is explicitly considered in the GFPM.
21DIN 52292-2:1986[81], which was used for the majority of tests performed in the past, has been replaced
by this standard. Apart from the suppression of the test setup R200, which was hardly ever used, it does not contain any relevant changes.
22The older German national standard DIN 55303-7:1996[84], which was used for many research projects