Damage monitoring in fracture mechanics by evaluation of the heat dissipated in the cyclic plastic zone ahead of the crack tip with thermal measurements
Introduction
Material fatigue behaviour in presence of crack depends on several factors related to the material and it is governed by different micro-mechanisms of damage at the crack tip. The first approach for describing the crack growth behaviour was proposed by Paris and Erdogan [1]. In their work the crack growth rate is expressed as a function of the stress intensity factor (SIF), [2]. In this regard, the constants of Paris’s Law can be obtained by use of conventional methods according to Standards [3], by means of experimental and non-destructive techniques [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18].
In the last years, many works [19], [20], [21], [22], [23] have focused their attention to the energy dissipated at the crack tip and to a possible relation with the growth of cracks. The energy based approach, proposed firstly by Weertman [19], links the crack growth rate with the critical energy to create a unit surface area. Moreover, this approach predicts a fourth power dependence of the crack growth rate and Stress Intensity Factor (SIF). Similar results were obtained by Klingbeil [20], where the crack growth in ductile solids is governed by the total cyclic plastic dissipation ahead of the crack. In [21] Mazari et al. starting from the Weertman’s and Klingbeil’s approach, developed a new model in which a similar Paris Law model was obtained between the crack growth and the heat dissipated per cycle.
The Dimensional Analysis approach was used in [22] to describe the fatigue crack growth rate as function of an energy parameter through a similar Paris-like model.
The experimental approaches used in literature aimed to determine the critical energy (Uc) were based on the use of strain gages in the plastic zone [23], [24], calorimetric measurements [25], and hysteresis loop evaluation [21]. However, these approaches require an off-line measurement and processing of data with consequent high testing time and cannot be applied on actual structural components.
Infrared Thermography (IRT) is a full-field contactless technique used in many fields such as, non-destructive testing (NDT), process monitoring and evaluation of heat sources during fatigue tests. This technique was already proposed for the study of the fracture behaviour of materials subjected to fatigue loading [11], [12], [13], [14], [15], [16], [17], [18]. In particular, a temperature rise due to the heat dissipations can be observed around the crack tip where the plastic zone is located. In this regard, Carrascal et al. [8] used IRT for evaluating the Paris Law constants of a polymer (polyamide) with an experimental methodology. A good agreement was found with respect to traditional calculation methods. Cui et al. [9], applied IRT to study the fatigue crack growth of magnesium alloy joints and demonstrated the potential of IRT in predicting the threshold value for unstable crack growth.
In the work of Meneghetti et al. [26], experimental tests were performed for evaluating the specific heat energy per cycle averaged in a small volume surrounding the crack tip from temperature measurements.
The above exposed procedures may find limitation in those cases in which temperature changes on material related to the plastic zone are very low (short cracks) and, moreover, high performance equipment and a difficult set-up are required. This is the case, for instance, with brittle materials (such as martensitic steels), welded joints and aluminum alloys [27], [28], [29].
Interesting results in assessment of plastic zone and SIF were obtained by using the Thermoelastic Stress Analysis (TSA) [30], [31], [32], [33], [34], [35], [36], [37]. By knowing the sum of the principal stresses, it is possible to determine the stress intensity factor and, at the same time, it is possible to determine the crack growth rate by analyzing the phase data. In this regard, Ancona et al. [38] proposed an automatic procedure based on TSA, to assess the Paris Law constants and to study the fracture behaviour of 4 stainless steels.
The aim of the work is to put the basis for a residual life estimation of a component in service conditions with a full field, contactless experimental technique able to determine the crack tip position and assess the dissipated energy per cycle. In this work, in particular, it will be presented the algorithm able to estimate the dissipated energy and define the crack tip position. Paris curve form thermographic data will allow a residual life estimation once the material is characterized.
Three CT steel (AISI 422) specimens were used and tested according to ASTM E 647-00 and the monitoring of crack tip growth was performed in a continuous manner by means of a cooled IR camera. Thermal data were processed in the frequency domain in order to extract the heat source related to the heat dissipated at the crack tip. Then, a simple method was used for estimating the heat energy dissipated per cycle. A similar Paris Law model was obtained between the crack growth and the heat dissipated per cycle. Moreover, it was obtained a fourth power dependence of heat dissipated energy and Stress Intensity Factor (SIF) in agreement with numerical and analytical models present in literature.
The proposed approach seems very promising for the on-line monitoring of crack growth during testing through a set-up which is simple compared to other techniques. Moreover, a simple specimen preparation is required, which makes the proposed procedure also suitable for the monitoring of actual structural components.
Section snippets
Theory
The heat dissipated per cycle surrounding the crack tip was evaluated taking into account a theoretical model proposed in [39]. It can be noticed in Fig. 1, that a control volume V contains the plastic area Ap of radius rp around the crack tip. In order to deal with a detailed analysis of all the effects affecting the material behaviour, it is possible to write the first law of thermodynamics, in the well-known form to describe such phenomena:where Wp represents the mechanical energy per
Specimen geometry and materials
The tested material is the martensitic steel AISI 422. The percentage of chromium is 11–13% in weight, and moreover, the presence of W, V and Mo alloys in the lattice, favorites the complex carbide precipitation. So, this steel can be tempered at relative high temperature (650 °C) without having chromium depleting of the lattice.
In Table 1, Table 2 are presented its chemical composition and the mechanical properties [42].
Three Compact Tension (CT) specimens were used with dimensions according to
Methods and data analysis
In the Section 3, it has been shown as the heat dissipation increases two time for cycle with a typical trend in the case of adiabatic conditions (Q = 0). In order to estimate the heat dissipated, it is necessary to detect the surface temperature of the specimen during the test. The temperature variations of the material associated to the Ed will be hereafter indicated as Td while the total temperature variation in one cycle as ΔTd (Fig. 2b)).
In this way, the energy dissipated per cycle and in a
Results and discussion
As described in previous sections, thermographic sequences were acquired during constant load intervals of 2000 cycles and coefficients T0, b and A were assessed through Eq. (10). The first two are related to the temperature rise ahead the crack tip due to the heat dissipated in the plastic volume. As already said, this heat can become difficult to assess due to heat exchanges for conduction, convection and radiation. The term A is more strictly related to dissipated energy.
Fig. 7 shows T0 maps
Conclusions
In this work, a new procedure based on the processing of thermographic data has been proposed for evaluating the crack growth rate through the assessment of heat dissipated at the crack tip during fracture mechanics tests continuously.
Three CT specimens of the martensitic stainless steel AISI 422 were tested and monitored by means of a cooled infrared camera in order to acquire thermographic sequences during tests at regular intervals (2000 cycles each).
The proposed procedure uses the analysis
Acknowledgements
This work is part of a large-scale research project (PON-SMATI) aimed at identifying innovative steels to turbo machinery used in extreme environmental conditions. The authors would like to thank GE oil & gas (Nuovo Pignone S.r.l.) for the support and collaboration provided in the experimental tests.
References (45)
- et al.
Three-dimensional analysis of fatigue crack propagation using X-Ray tomography, digital volume correlation and extended finite element simulations
Proc IUTAM
(2012) - et al.
Quantifying crack tip displacement fields with DIC
Eng Fract Mech
(2010) - et al.
Dynamic full field measurements of crack tip temperatures
Eng Fract Mech
(2001) - et al.
Dissipative and microstructural effects associated with fatigue crack initiation on an Armco iron
Int J Fatigue
(2014) Linear fracture mechanics, fracture transition and fracture control
Eng Fract Mech
(1968)- Paris P, Erdogan F. A critical analysis of crack propagation laws. J Basic Eng, Trans Am Soc Mech Engineers, 1963; D...
- Ritchie RO. Mechanisms of fatigue-crack propagation in ductile and brittle solids. Int J Fract 1999;...
- ASTM E 647–00: Standard Test Method for Measurement of Fatigue Crack Growth Rates,...
- et al.
Observation of Magnetic Flux Density Distribution around Fatigue Crack and Application to Non-Destructive Evaluation of Stress Intensity Factor
Proc Eng
(2011) - et al.
Determination of the Paris’ law constants by means of infrared thermographic techniques
Polym Testing
(2014)
Research on fatigue crack growth beahavior of AZ31B magnesium alloy electron beam welded joints based on temperature distribution around the crack tip
Eng Fract Mech
Infrared thermography study of the fatigue crack propagation
Frattura ed Integrità Strutturale
Thermoelasticity for the analysis of crack tip stress fields – a review
Strain
Measuring stress intensity factors during fatigue crack growth using thermoelasticity
Fract Eng Mater Struct
Some improvements in the analysis of fatigue cracks using thermoelasticity
Int J Fatigue
Application of thermoelastic stress analysis for the experimental evaluation of the effective stress intensity factor
Frattura ed Integrità Strutturale
Crack growth monitoring in stainless steels by means of TSA technique
Proc Eng
Experimental study of the crack growth in stainless steels using thermal methods
Proc Eng
Theory of fatigue crack growth based on a BCS crack theory with work hardening
Int J Fatigue
A total dissipated energy theory of fatigue crack growth in ductile solids
Int J Fatigue
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