MATERIAL SIMULATION AND DAMAGE ANALYSIS AT
THERMAL SHOCK CONDITIONS
Franz-Barthold Gockel, Rolf Mahnken, Ferdinand Ferber
Chair of Engineering Mechanics (LTM), University of Paderborn,
Warburger Str. 100, D-33098 Paderborn
franz-barthold.gockel@LTM.uni-paderborn.de
Summary
Thermal shock is an extreme form of thermo-mechanical loading. Detailed investigations of
thermal shock and live time analysis close to reality are necessary in industrial engineering in
order to get a good prediction of life expectancy of high quality and safety relevant machine
components. The first part of this paper concentrates on experimental investigations of
macroscopic quantities like cyclic deformation, damage and crack propagation. For this purpose
cylindrical specimens of a heat resistant steel (X15CrNiSi20-12) are heated by natural gas burner
and shocked down by water quench in a cyclic manner. An optical 3-dimensional digitalisation
system enables the full surface measurement of deformation resulting from temperature
conditions and the number of load cycles. The eddy current method is used to determine
structure changes in material and crack propagation. Additionally results on the parameter
identification for the Chaboche material model are presented on the basis of uniaxial cyclic
experiments and the finite element simulation of the thermo-mechanical problem of thermal
shock is presented for a cylindrical specimen.
Introduction thermal shock and experiments
Many modern components and structures in industrial engineering are subjected to thermomechanical loading. Within the interaction of analytical, experimental and numerical
investigations, basic data are required which characterize the grade of thermal shock loading [1],
[2]. This paper gives an overview of thermal shock experimental deformation and damage
analysis and parameter identification to utilize this knowledge for finite element simulations. The
tested material is a heat resistant austenitc stainless steel X15CrNiSi20-12 (1.4828), which is
used in many high temperature applications. The thermal shock tested specimens were heated up
to 820°C by a natural gas burner within 10 minutes und were shocked down in a water quench
basin to nearly room temperature in 1 Minute. Every hundred thermal shocks a break for
measurement of deformation and danage analysis was implemented in the experimental process.
For the geometric measurement a 3-dimensional digitalisation system is in operation and for the
analysis of crack damages in the specimens surface the eddy current system is used. The results
of deformation measurement and of the damage analysis after the application of thermal shock
load give at first knowledge of effects of thermal shock as reference date for product engineering
and these date will be used in addition for the formulation and validation of simulation models
for the prediction of deformation and damage in extrem thermo-mechnical loaded components.
Deformation measurement by 3D-digitalisation
The cyclic applications of thermal shocks cause plastic deformations with magnitudes of
several 1/10mm. Typical tolerances which are usual for machine components are overshot and
the geometrical form of the cylinder gets uneven. The technique of the 3-dimensional
digitalisation of the thermal shocked specimen surface, used in the executed experiments,
enables a geometric analysis for the full body of the tested cylinder by a camera system. A
representative result of the plastic deformation after cyclic thermal shocks is shown in Fig. 1 in
comparison for different load cycles up to 700 thermal shocks. The degree of deformation and its
characteristic are important parameters for the evaluation of functional quality and for
comparison to simulations of thermo-mechanical loaded components. The comparison of the 3Dmodels at different numbers of thermal shock cycles presents the dimensional differences as it is
illustrated in Fig 1 on the right side. For closer examinations cross section are done and those
deliver the profil of the thermal shock specimen. In fig. 1, on the left side, the development of
deformation for a selected single line of the cylinder surface is presented, starting at 3 thermal
shock cycles up to 700. The results in Fig. 1 illustrate the typical type and magnitude of
deformation. At the top and the bottom of the specimen the diameter and length are increased,
whereas at other areas a decrease of diameter and length is observed, thus resulting into a „Wshape“ deformation form. The magnitude and the characteristic of deformation are reproducable
for different specimens and over the whole range of realiesed numbers of thermal shock cycles.
So the cross section diagrams, fig. 1, and the 3-dimensional models of digitalisated test cylindes,
fig. 2, are a reference for principle discussions of thermal shock load and for the validation of
material models for simulation of thermal shock conditions. The experimental data of the 3Ddigitalisation can be compared to simulations for the full surface of the specimen.
FIGURE 1 Development of deformation of thermal shock specimen 17 in correspondence to
thermal shock cycles for a line on the cylinder surface on the left side, and a 3Ddifference model with a selected cross section of the model
The plastic deformation of the tested cylinder depends on the number of thermal shock cycles.
The maximum difference of radius should be handled as the value of assumption of plastic
deformation. The observation gives the development engineer a chance to realise the effect of
cyclic thermo-mechanical load. The transmission to applications of similar geometry or load
conditions should be realised by model calculations. Those model calculations should use
material models, which are able to reproduce the deformations in correspondence to the load
conditions. In the third part of this paper, these experimental results of the deformation analysis
are used as a quality standard for the simulation of the thermal shock experiment.
FIGURE 2 The 3-dimensional digitalisation of the development of deformation of a thermal
shock cylinder specimen
Damage analysis by eddy current method
In the first step phenomenological investigations of initiated damage give an overview of the
consequences of cyclic thermal shock conditions. Excellent surfaces quality at the begin of the
experiment, change to a rough surface after less than a hundred thermal shocks and after
hundreds of cycles it changes to a cracked surface of the specimen.
4 mm
a)
b)
FIGURE 3 a) structured surface of thermal shock loaded specimen with the characteristic spider
network of micro damage initiation, damage phase 1 b) macroscopic crack after 700
thermal shocks, damage phase 2.
The development of damage starts by structure changes and micro cracks in a spider network
manner, as it is typical for thermal shock load. These micro cracks are the starter notches for
macro crack propagation. After 400 thermal shocks a microscopic examination of the specimen
surface is presented in fig. 3a). In the centre of this photo a characteristic notch for the initiation
of macro crack propagation can be seen. By an additional number of thermal shocks a reticulated
damage structure grows up to macroscopic crack propagation at single locations, as presented in
fig. 3b). These surface inspections deliver knowledge of the long-term effect of thermal shocked
materials in product engineering. In addition to the before analysed deformations the useful
properties are also influenced by surface structure effects and damage propagation.
To acquire the degree und location of surface structure changes and damage of the thermal
shocked cylinders, those specimens were analysed in recurring eddy current checks. The eddy
current check, which is approved in industrial quality control, makes use of impedance changes
of the inductive system of sensor and specimen, caused by micro structure changes and damages,
so different effects of material properties can be detected by the eddy current test. Fig. 4b)
presents the test configuration of the thermal shocked cylinder, rotated by a lathe and the eddy
current sensor in differential operation. A typical section of the measurement results, the absolut
value of the impedance signal, is presented in fig. 4a). The noise of the signal lower than the
low-level mark represents roughness depth, effected by the cyclic thermal shocks. By increase
the number of thermal shock cycles the amplitude of the eddy current signals groves up. After
several hundred thermal shocks macroscopic cracks can be identified by high-level signals of the
damage analysis. Due to the phenomenological inspection of fig. 3 and the results of the eddy
current signal, in the following discussion the damage evolution should be divided into two
phases. The damage phase 1 includes the load sequence up to micro cracks, which do not cross
in maximum the low-level mark in fig. 4. The second phase of damage evolution incorporates
those damages, which cause eddy current signals crossing the low-level mark of fig. 4, which
represents the initiation und propagation of macro cracks.
a)
b)
FIGURE 4a) Value of the eddy current signal for one circle line of the checked surface of the
specimen with definition of different signal levels. b) Arrangement of the eddy current
sensor and the rotating thermal shock specimen.
After scanning the whole surface of the thermal shock specimen by the eddy current system
with respect to the two defined damage evolution phases, fig. 5 presents micro crack propagation
in the first half of the experiment and macro crack propagation in the second half of the
experiment. After 400 thermal shocks, which corresponds to a deformation difference of 0.6mm,
the number of detected micro cracks decreases and the eddy current signals of phase 2 signals
increase. From this status of damage (400 cycles), the micro crack initiation stops and the micro
cracks grove up to macro cracks, as it can be seen in fig. 5 (cycle number 400 up to 500) in the
last part of the diagram.
FIGURE 5 a) accumulated eddy current signals divided into the phase of micro cracks and macro
cracks over the number of thermal shock cycles.
With respect to the experience of common damage theories the results of fig. 1 and fig. 5 can
be used in combination to get a dataset of degree of damage depending on plastic deformation. It
is the attention to formulate rules to predict damage evolution for thermal shock conditions on
the base of these presented results of deformation and damage analysis. In addition to the
assumption of crack signals detected by the eddy current check system, the location of damage
initiation and propagation is an issue of interest. In fig. 6 the results of the whole surface damage
analysis are projected onto the digital model of the thermal shock experiment. By this instrument
the influence of geometry and boundary conditions can be examined, and this experience can be
transmitted to the product engineering of high temperature loaded equipment.
Eddy current
signals of
macroscopic level
damage phase 2
FIGURE 6 Projection of the eddy current signals onto the digital surface of the thermal shock
cylinder specimen after 500 thermal shocks, diameter 60mm, length 60mm, material
1.4828
Uniaxial experiments, parameter identification and simulation
In the next step, it is the concern to simulate to simulate thermo-mechanical load by the use of
the finite element method. Therefore an adequate material model has to be available. Such a
material model can be formulated and implemented individual or the proposal of commercial
finite element programs can be used. To find out the required material properties for the use in
material simulations, uniaxial cyclic tests have been done. In the corresponding cyclic stress
strain diagram, Fig.2 the hysterese loops show a significant temperature dependency of the stress
strain relation. In the experiments different constant temperatures between 20°C and 900°C and
strain rates of 2%/min and 20%/min are realised to get a corresponding data base for the whole
temperature range of the thermal shock experiments presented above. A closer examination of
the hysterese loops show hardening and softening effects, which depend on the actual cycle
number. On the basis of the experimental data, fig. 1 and fig. 7 the chaboche material model [3],
[4] allows to consider phenomena as:
•
elasticity
•
plasticity,
•
hardening,
•
softening,
•
rate dependence of material properties and
•
temperature dependence of material properties
by the set of constitutive equations.
From tension tests and the analysis of the hysterese loops (fig. 7) rate dependence of the yield
stress and rate dependence of the strain stress loops for the high temperature experiments can be
identified. The yield stress and the hardening characteristic depends on the test temperature.
FIGURE 7 Hysterese loops of the uniaxial tension and compression experiment at a temperature
of 20°C and 900°C an da atrain rate of 2%/min and 20%/min
FIGURE 8 Procedure of parameter identification and optimization for the chaboche material
model
For considering the mentioned material effects of the thermal shock experiment, the material
model of chaboche was chosen to realise a simulation of the thermal shocked cylinder, as used in
the experiments. For identification and optimization of the associated material parameters of the
chaboche model a simulation of the uniaxial cyclic experiment and the corresponding experiment
were compared to each other in the verification process by the use of the least square method. In
the optimization loops the eight parameters are adjusted until a reasonable quality is obtained.
The parameter identification process, including the optimization loop, is presented in fig. 8. The
required initial values for the start of the identification process, as for example the young’s
modulus or the yield stress, can be taken from the first evaluations of the uniaxial experiments or
have to be assumed. In each iteration step the simulated numerical result of the stress- strain
relation is compared to the equivalent step of the corresponding experiment. By undercut of the
defined error margin the material parameter of the use material model are identified and are
available for implementation in simulations of high temperature loaded machine components.
The results of the verification process for the material 1.4828 can be seen in fig. 8, at a test
temperature of 900°C for the first load cycle on the left side and for the 50th load cycle on the
right side at a strain rate of 2%/min.
a)
b)
FIGURE 9 Verification of the parameterized chaboche material model for the uniaxial cyclic
tenson-compression test, at 900°C, strain rate 2%/min, material 1.4828
Both diagrams of fig. 9 show good accordance between simulation and experiment of the
uniaxial cyclic tension compression experiment, which is a minimum requirement for application
in assimilable simulations, e.g. thermo-mechanical load by thermal shock. The parameter
identification has been done for each of the five realized constant test temperatures in the range
of 20°C and 900°C and for each of these temperature steps an individual set of material
parameters is available. These identified material parameters were transmitted to the finite
element model of the thermal shock loaded cylinder. The plastic deformation, as the simulation
result, is presented in fig. 10 in comparison to the corresponding thermal shock experiments. In
this process of validation of the parameterized chaboche material model, the simulation of
thermal shock load and the thermal shock experiment are independent of each other. In this step
of validation, the quality of the material model, to predict thermal shock load, is shown. Between
15mm and 45mm length, good accordance in quality and quantity can be achieved. At the top
and the bottom of the specimen, there are significant discrepancies in the quantity result. This
validation of the parameterized chaboche model makes clear, that the parameter identification
and quality check in the verification in the direct dependency between simulation and
experiment, fig. 8, is a necessary criterion but not sufficient. Not until simulations satisfy
independent experiments, those simulation models should be used in practice for similar
problems. The validation in fig. 10 makes clear, that there is additional optimization potential for
the finite element model or the parameterized material model.
FIGURE 10 Results of the validation of the parameterized chaboche model, comparison between
simulation and experiment after 400 thermal shock cycles.
Summary and Conclusion
•
•
The measurement of the plastic deformation after cyclic thermal shock load conditions by the
use of the 3D-digitalisation method delivers experimental data for the validation of
simulation models and as a reference value for similar thermal shock applications.
Crack propagation and surface damage after cyclic thermal shocks are localised by the eddy
current method. The degree and location of thermal shock damage is presented by an
accumulation of the detected eddy current signals depending on the load cycle number and
by the projection of the eddy current signals to the 3-dimensional digitalisation of the
•
•
•
•
specimen. These damage analysis data of thermal shock loaded specimens are a basis for the
formulation of live time prediction calculations.
Parameter identification was made for the Chaboche model by the use of uniaxial
experimental cyclic strain stress data at different temperature levels.
The implementation of the parameterized chaboche material model into the finite element
simulation of the thermal shock loaded cylinder provides partly accordance of the
experimental evaluation of plastic deformation and the corresponding simulation by the finite
element method.
The experimental work will be supported in future by an automated test equipment. The
cyclic thermal shock experiments including the 3-dimensional deformation measurement and
the eddy current control will be executed by an automated process management, so it will be
possible to create a reproducible database with a data volume for statistic evaluations.
Future work will concentrate on the optimization of the finite element simulation of thermal
shock problem. In addition damage models have to be developed and implemented for
prediction of the evolution of damage and crack propagation corresponding to the number of
thermo-mechanical load cycles.
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