Investigation of Strain Effect on Cleavage Fracture for Reactor Pressure Vessel Material

*Kushal Bhattacharyya*

### **Abstract**

Failure mechanism of 20MnMoNi55 steel in the lower self of ductile to brittle transition (DBT) region is considered as brittle fracture but it has been observed from the experimental analysis of stress-strain diagram that clear plastic deformation is shown by the material before failure. Therefore, strain correction is implemented in the cleavage fracture model proposed by different researchers in the lower self of the DBT region with the help of finite element analysis. To avoid a huge number of experiments being performed, Monte Carlo simulation is used to generate a huge number of random data at different temperatures in the lower self of the DBT region for calibration of the cleavage parameters with the help of the master curve methodology. Fracture toughness calculated after strain correction through different models are validated with experimental results for the different probability of failures.

**Keywords:** fracture toughness, plastic strain, reactor pressure vessel, master curve, finite element analysis

#### **1. Introduction**

Regular maintenance of the reactor pressure vessel (RPV) is an important criterion that has to be considered where safety is the prime requirement for any country. In that respect embrittlement of the RPV material has to be quantified concerning reference temperature *T*0. In the last few decades, several researchers tried to quantify this embrittlement nature of ferritic steel in RPV materials. Among them, the work done by Kim Wallin with the development of ASTM E1921 and master curve [1–3] proved to be quite impressive and acceptable in quantifying embrittlement for different ferritic steels used in reactor pressure vessels with the help of reference temperature *T*0.

It has been observed in our previous work that references temperature (*T*0) predicted for 20MnMoNi55 steel is constraint dependent [4] and it varies with different crack length, thickness, and geometry of the specimen. It also shows the variation with test temperature and censor parameter "m".

This observation is also predicted by different researchers [5–10] working in this field of ductile to brittle transition (DBT) region for different RPV materials.

Therefore, in the last few years, the main aim of the researchers was focused to study the constraint effects of reference temperature *T*<sup>0</sup> for RPV materials. Finite element analysis is considered a useful tool to study the stress distribution near the crack tip of the specimen at different temperatures in the DBT region. With this aim in mind some researchers try to capture the constraint effect with the help of T-stress [11–15], Q-stress [16–18] and triaxiality [19]. The author also tried to capture the loss of constraint effect on the reference temperature *T*<sup>0</sup> for these RPV materials with the help of these three stress-based parameters in his earlier work [20]. A satisfactory correlation of the constraint effect in the upper domain of the ductile failure-dominated region of the DBT region is observed. But the brittle failure-dominated region or the lower transition region remains untouched. Therefore, many researchers tried to address the lower transition region with different cleavage failure models. Among them, the work is done by Beremin [21] and his co-authors prove to be challenging for the RPV materials at the brittle failuredominated portion of the DBT region. The author is motivated to explore a brittle failure model to capture the constraint effect satisfactorily in the lower transition region. With that framework in mind, the widely accepted Beremin model [21] is used to study the constraint effect on master curve and reference temperature (*T*0) by different researchers for 20 years or more. Beremin cleavage fracture model provides a good correlation between localized stress pattern prevailing near the crack tip with that of global parameters of fracture like J-integral, applied to load, and fracture toughness with the help of Weibull stress a parameter of stress as coined by Beremin. But the calibration of the constant parameters which remain unique for the material is a challenging job because it demands to test more than 30 specimens to predict a reliable result as predicted by Khalili and Kromp [22]. But testing such a huge number of tests for a given material and at a given test temperature is much expensive. Therefore, many authors utilized the Monta Carlo simulation to generate a huge random number of data from the 6 experimental fracture toughness results to determine the parameters at different temperatures. The entire process is explained in the author's previous work [23].

Beremin model is entirely focused on brittle fracture where no strained effect is considered but it has been observed in the experimental stres-strain diagram for the material 20MnMoNi55 steel a huge plastic deformation is observed in the material before failure even at 110°C and the plastic region diminishes as it moves towards 150°C. Therefore, strain correction is required in the model for proper calibration of the Beremin parameters for the material. Beremin himself in his work felt the requirement for strain correction and he simultaneously developed a model considering the effect of strain in calculating Weibull Stress [21]. Recently, Ruggieri in his work [24, 25] utilized the strain effect by different models for a similar type of RPV material A515 Gr 65 pressure vessel steel. But he uses the toughness scaling model to calibrate the Beremin model parameters.

In December 2017, Claudio Ruggieri, Robert H. Dodds Jr. [26] through their work focuses on the importance of plastic strain effects into the probabilistic framework in brittle fracture.

In November 2019, Claudio Ruggieri [27] through his work proposed a probabilistic, micromechanics-based model which incorporates plastic strain effects on cleavage fracture and its dependence on the microcrack distribution. The model utilized a plastic-strain based form of the Weibull stress to capture the differences in brittle fracture toughness for a reactor pressure vessel (RPV) steel due to constraint loss.

In the present work fracture toughness of 20MnMoNi55 steel is determined with the help of three-point bending (TPB) at 100°C, 110°C, 120°C, 130°C, *Investigation of Strain Effect on Cleavage Fracture for Reactor Pressure Vessel Material DOI: http://dx.doi.org/10.5772/intechopen.101245*

140°C, at reference temperature *T*<sup>0</sup> and master curve is calculated for all of this results. Then elastoplastic finite element analysis of each fracture specimen is performed taking the boundary condition from the experimental results. The stressstrain diagram obtained from the test performed by the previous researchers [27] for this material, provides the material properties required for the FEA. Beremin model parameters are calculated using strain correction as proposed by the modified Beremin model, local criterion using the distribution of particle fracture stress, following exponential dependence of eligible microcracks on ϵ<sup>p</sup> (plastic strain) and under influence of plastic strain on microcrack density. The Weibull modulus (m) and Webull scale parameter (σu) are calibrated by Monte Carlo simulation for temperatures 100°C, 110°C, 120°C, 130°C, 140°C from the experimental results as explained in the previous work [24]. Then Cm,n another Beremin parameter is also calibrated for the above-mentioned temperatures as described in the previous work of the author [28]. Once the Cm,n is calculated fracture toughness can be predicted for different temperatures from the above-mentioned models for different probability of failures. The predicted fracture toughness is compared with the experimental values.

In this work, the entire focus is being made on the brittle failure nature of German based reactor pressure vessel material (20MnMoNi 55 steel) at the lower self of DBT region, which is a very important study as far the safety of reactor pressure vessel is concerned. In recent years study on this material dealing with specific topics is not performed. Moreover, the application of Monte Carlo simulation to reduce the burden of performing a huge number of fracture experiments is overcome by this procedure. The author proves the success in the application of the statistical model by matching it with the experimental results in his previous work [29]. In the present work, the author utilizes the statistical model along with FEA to study the effect of strain on brittle fracture through four different strain corrected brittle fracture models. In the end, the fracture toughness predicted from these models is compared with the established ASTM E1921 and master curve results which is a very challenging and interesting part of the work.
