Fracture toughness on compact tension specimen as a quality parameter for cement stone

A series of tests of compression strength and fracture toughness of hardened cement paste (cement stone) was carried out. The compression strength was tested on cubes with side lengths of 10, 20, 30 and 40 mm. Fracture toughness was measured on compact tension (CT) specimens with dimensions commonly used in metallurgy; two different thicknesses were used (h x l x b: 50 x 48 x 3 mm3 and 50 x 48 x 8 mm3). A particularly stiff piezo‐controlled test frame was used as testing device. The different thicknesses of the specimens allow the investigation of a possible size effect in toughness. In a Weibull statistical evaluation, the scatter of the strength results is compared with the scatter of the measured toughnesses. It could be shown that the fracture toughness results are as reliable as the strength results and the method is a useful addition to the research on fracture of binders.


Introduction
The production of cement generates high amounts of CO2 and, therefore, takes part in the global climate crisis.This has generated increased research into new binders with the aim of lowering the emissions of concrete, a building material that can hardly be replaced.In everyday construction, over 4 billion tons of cement are consumed annually [1].Here, availability is not an issue.In contrast, research projects can be affected by limited quantities of material available for testing purposes.There are many reasons for this; limited production capacities for new binders, the number of production steps, and waiting times.The aim of this work is to find a parameter to determine the quality of hardened cement paste at the laboratory scale.
When testing the fracture mechanical quality of cement, it is mainly determined by the compressive strength tests on mortar prisms according to .This test is not always applicable in research due to the required material quantities.These arise from the sample size itself, but also the number of samples to be tested due to the natural scatter of results.
A first possibility to reduce the material consumption would be to test the compressive strength on smaller cubes.For quasi-brittle materials such as cement stone, two effects have to be considered.First, there is always a scatter in the results of fracture strength at the same loading conditions.For cement stone, the variation itself is based on the defects inside the material.Defects are imperfections caused by hydration, different material properties of the components and due to manufacturingrelated causes, such as microcracks, or gel -, capillaryand compaction pores [3].The specimen size has an effect on the degree of variation due to the statistical probability of certain defects to occur in the tested volume [4].Second, when reducing the specimen size, the occurrence of a size effect is to be expected.It describes the inverse relationship between the nominal strength and the geometric size of specimens.The investigation of concrete components shows both effects.The scatter of the strength and the average compressive strength decrease with increasing component size [5].In his book, Bažant describes various reasons for the occurrence of a size effect.Most of the times it has statistical reasons but also hydration phenomena can be responsible [4].While many studies focus on the size effect of concrete and mortar, Su was able to show in an extensive series of tests that a size effect also exists for the compression strength of hardened cement paste [6].Research about the sizing of specimens also often focuses on concrete.The edge length of a specimen depends on its maximum grain size [7].Conditions for the minimum size of a cement stone specimen have not been elaborated on.
A second option besides reducing the size of the compression specimen to save material is to research what other parameters can be tested in fracture mechanics.A common parameter is the fracture toughness.It is defined as the resistance of a material to crack propagation.Toughness and strength are directly linked to each other.

Abstract
A series of tests of compression strength and fracture toughness of hardened cement paste (cement stone) was carried out.The compression strength was tested on cubes with side lengths of 10, 20, 30 and 40 mm.Fracture toughness was measured on compact tension (CT) specimens with dimensions commonly used in metallurgy; two different thicknesses were used (h x l x b: 50 x 48 x 3 mm³ and 50 x 48 x 8 mm³).A particularly stiff piezo-controlled test frame was used as testing device.The different thicknesses of the specimens allow the investigation of a possible size effect in toughness.In a Weibull statistical evaluation, the scatter of the strength results is compared with the scatter of the measured toughnesses.It could be shown that the fracture toughness results are as reliable as the strength results and the method is a useful addition to the research on fracture of binders.
Strength is a parameter that comprises the fracture toughness and the defects in the tested volume.Toughness of concrete has been analyzed experimentally and numerically on many different specimen geometries, including notched beams and disc-shaped compact tension specimens [8,9,10].However, the material cost due to the specimen size is just as great, if not greater than the original prisms for testing compressive strength of cement.
An evaluation of experimental fracture data to give information about the reliability of such results is necessary.Commonly used is the statistical Weibull analysis.It is widely used to characterize the statistical variation, e.g. the fracture strength of ceramics [11].It is a common tool in concrete fracture as well to analyze both, fracture toughness and strength.Li et al. were able to predict peak loads of concrete strength and toughness with a 95 % reliability using the three-parameter Weibull model [12].There are many other examples, especially for the analysis of strength.As a central question it is regularly discussed, whether the Weibull distribution is the best fit for the experimental data [13,14].
To define the mechanical properties, an alternative from metallurgy was conducted within this work: the testing of fracture toughness on compact tension specimens [15].With a volume of about 19 cm³, the material requirement for these specimens is many times smaller than that of the prisms, which require about 256 cm³.In addition, the compressive strength was tested on cubes of different sizes and the results were evaluated using Weibull analysis.

2
Experimental work

Sample preparation
Portland cement CEM I 52.5 R from Wittekind (Hugo Miebach Söhne KG) is used in this study.All specimens consist of pure cement paste with a water to cement ration of 0.5.They were cured for 1 day at room temperature while covered in a moisture-saturated surrounding, and then cured a further 27 days in water.Compact specimen of two different sizes were used for testing the fracture toughness (see Table 1).Each data set consists of at minimum 20 specimens.Due to damage during the sample manufacturing process, the total number varies.This mainly affects the CT specimens.
Right after preparation of the cement paste, the specimens were moulded in two layers and compacted on a vibrating plate to form a single sample.The moulds and an example of the finished specimen are shown in Figure 1.After demoulding, the specimens were cured before being used in the experiments.The dimensions of the cubes for compression testing are determined.The cubes are tested as is.The specimen for compact tension testing, however, are not.While they have the necessary holes for inserting the supports, the sample itself is usually too uneven to fit into the piezo frame and a notch between the holes is missing.Thus, the sample were ground even, a notch was created via a circular saw, and a crack at the bottom of the notch was made using a sharp blade.The load value is measured at which the material fails.The dimensions of the compact specimens are based on the standards for the testing of fracture toughness of metallic and ceramic materials [15].The selected length ratios are shown in Figure 2. Specifications on the thickness of the specimen were neglected due to lack of plastic zone in cement paste, a quasi-brittle material.

Compression tests
To test compression strength, a hydraulic press from the company Walter + Bai AG with a maximum load of 300 kN was used.The specimens were placed between two parallel plates, which were loaded with a controlled loading rate of 2400 N/s until fracture.The maximum load before failure was automatically documented by the press.
The plate-shaped inserts for the press were available in size 40 x 40 mm as well as 30 x 30 mm.The surface area A was determined individually for each cube and used to calculate the compressive strength using the equation below Where Rc is the compressive strength in mPa Fc is the maximum load at fracture in N A is the surface area of the cube in mm 2 .

Toughness measurement
The fracture toughness testing set-up includes an ARCO-CT device (Advanced Rigid Crack Opening on CT-samples) built by Rödel & Isaia GmbH.The device is placed under a Keyence VHX digital microscope yielding the microscopic image during the test.The ARCO-CT device can be seen in Figure 3.It consists of an extra rigid frame with a fixed support arm including a solid state hinge (left upper corner).Two U-shaped grips transfer the load to the bores in the CT-samples.One of the grips includes a load cell in series.The specimen is inserted into the frame using two pins and preloaded using preload rods.The PI P-025.80 piezo actuator is connected to an electric power supply.Due to the high stiffness of the frame and the actuator, a displacement controlled setup is generated this way.The load onto the specimen is increased via increasing voltage.Once the crack starts to propagate, the load slightly drops.This is the control feedback for advancing the crack at constant stress intensity factor by immediately reducing the load slightly.
The crack propagation is not necessarily visible on the specimen surface in the case of hardened cement paste, because not all specimens fracture completely.Through their thickness.Accordingly, crack propagation is detected with the help of the recorded stress.As soon as the crack progresses, the stress recorded with the load cell decreases even though the voltage on the piezostack remains.This is an advantage of the displacement control.The operating principle of the measurement is shown in Figure 4.After the measurement, microscope imaging is used to determine the crack propagated from the crack tip of the specimen.This ensures that the test is valid.
If this is the case, the fracture toughness of the material can be calculated from the specimen dimensions and the maximum stress before failure: where KQ is the fracture toughness in MPa m 0.5 FQ is the maximum load at fracture in N B is the specimen thickness in mm (3) where a0 is the initial crack length in mm and W is the width of the specimen in mm.

Estimation of Weibull parameters
To describe the probabilistic behavior of the strength as well as the fracture toughness, the experimental data sets were analyzed according to the two-parameter Weibull distribution [16].The cumulative distribution function that gives the probability of failure F(σc) at a load level σc is given by The values of each data set were ranked from lowest to highest.Each value was assigned a value for the cumulative probability of occurrence based on the ranking from 1 to n, where n is the total number of specimens tested.That way each measurement is assigned a failure probability Fi, which reads as follows Subsequently, Equation ( 4) can be rearranged and (doubly) logarithmized into ln ln After plotting ln [ln 1/(1-F)] against ln (σc) the data can be fitted by linear regression.The slope of these lines yields the Weibull modulus.

Results and discussion
The mean values of the results, the standard deviation, as well as the corresponding Weibull moduli for each data set are given in Table 2.A minimum of 30 specimens were tested for the compression strength while a minimum of 20 specimens were tested for fracture toughness.
The mean values of the compression strengths for cubes with edge lengths of 20, 30, and 40 mm are similar.Values range around 70 MPa.The average value of the smallest cubes with a size of 10 mm shows a significantly lower value.This observation indicates that the size of the cube has an effect on the compression strength.A size effect was to be expected, but according to Bažants' size effect theory the compression strength should be higher for smaller specimens which is not the case.It is worth noting that many phenomena that Bažant considers responsible for the size effect are typically exhibited on much larger specimens.The volumes tested by Su et al. have a side length of 40-200 mm [5].The dimensions of the cubes tested in this study are significantly smaller.To assess the results satisfactorily, it is necessary to investigate the early failure of the smallest cubes in more detail.One possible reason is the rate of hydration.Too fast drying of the specimens leads to large primary cracks and thus small strengths.A further investigation could focus on the relationship between the defect size and the volume size of the specimen.If necessary, the minimal specimen size must be restricted based on the relationship between defect and volume size.The accumulated Weibull probability plots of compressive strength are shown in Figure 5. Within a range from 4.3 for the smallest to 9.3 for the biggest cubes, the Weibull modulus, which describes the scatter of results, decreases as the size of the cubes decreases.This trend is in accordance with literature.The scatter and standard deviation of the results is bigger for smaller specimens.This is due to the probability of certain defects to be present in the tested volume.For bigger specimen the probability of having a similar defect size distribution in each sample of a data set is bigger.For small specimens, the size of the largest defect leading to failure varies more.This can be seen in the scatter.
The answer to the original question, as to whether the specimen size for the compression strength can be  The mean values of the fracture toughness tests were found to be similar for both specimen thicknesses.The values 3.2 MPa m 0.5 and 4.5 MPa m 0.5 fall within a realistic range when compared to values from literature [12,17].However, the results are not yet significant enough to rule out a size effect in fracture toughness.

Experiment
The Weibull probability plot of the fracture toughness is shown in Figure 6.With Weibull modules of 5.1 and 6.0 the scatter of the fracture toughness is a little higher than the compression strength results with standard edge length of 40 mm.In comparison to fracture toughness tests on concrete and mortar specimens from other researches [8,9,10], the use of smaller specimen sizes in this study is advantageous in terms of reducing the amount of material required for testing.Additionally, the smaller specimens allow for testing under microscopic observation, which can provide valuable information about crack propagation details.
Testing under a microscope allows for detailed observation of crack propagation.Figure 7 shows a microscopic image of a compact tension specimen right after crack advance (left).A drop of the load level proves crack propagation, but this is not yet visible at the tip of the notch.It only becomes visible after additional widening of the crack (right).This detailed view under the microscope helps validating crack propagation at the artificially induced crack tip.

Conclusions
In summary, it could be shown that the measurement of the fracture toughness of hardened cement paste with compact tension specimen is advantageous for research on new binders due to the very small amounts of material necessary.
The aim of testing the fracture mechanical quality and saving material by reducing the size of the specimens for compressive strength works to a limited extent, because the scatter increases with smaller specimen and a reversed size effect has yet to be explained.
The measurement of the fracture toughness provides satisfactory results for both geometries, whereby based on the scatter, thinner, i.e. less material-intensive test specimens provide the more reliable values.
While the fracture toughness is a complex parameter, which has only limited significance for concrete due to the heterogeneity of the system, it is a beneficial parameter for comparing the quality of new binders, which, when mixed only with water, can be treated as homogeneous.
For new binders, testing of fracture toughness is important.It is the actual material property which is different among different cements.Furthermore, the defect structure of new binders is probably different for common cement stone, so knowing the fracture toughness can help analyse strength results in more detail.
According to the current state of research, there is little scope for material savings when measuring compressive strength.However, the measurement of toughness on compact tension specimens is a very useful addition to the evaluation of the fracture mechanical quality of binders.
of two component polyurethane, VytaFlex 40, KauPo Plankenhorn e.K., were produced in the various sizes for specimen fabrication.The test program includes six different specimen sizes for the experiments.Cubes of four different sizes were tested for compression strength.

Figure 1
Figure 1 Silicon moulds and examples of the resulting specimen.

Figure 2
Figure 2 Compact tension specimen details

Figure 3
Figure 3 Example of a compact specimen in the ARCO CT device

Figure 4
Figure 4 Principle of measuring the fracture toughness on a compact tension specimen

)
is the stress intensity factor coefficient.The stress intensity factor can be calculated with the initial crack length and the width of the specimen[15]

)
0 represents the stress level that causes failure in 63.2 % of all cases.The parameter m is the Weibull module.It describes the scatter of the results.The larger m, the narrower the distribution.Hence, as m → ∞ the experimental data show no scatter at all.

Figure 5
Figure 5 Accumulated Weibull probability plots for compression strengths for cubes of different sizes laboratory scale, is not clear.Regarding the scatter of results, the study of compression strength could be performed on smaller samples with reliable results.The occurrence of the reversed size effect speaks against a reduction of the tested volume.It would have to be found out what triggers the effect microscopically.Furthermore, all literature values are based on 40 x 40 x 40 mm samples, which is why a reduction limits the comparability.

Figure 6
Figure 6 Accumulated Weibull probability plots for fracture toughness of compact specimens in different thicknesses.KI-values are given in MPa m 0.5

Figure 7
Figure 7 Microscope image of the specimen after crack advance (left) and after artificial widening of the crack for validation/ verification/ review (right)

Table 1
Test program

Table 2
Main results