Engineering Fracture Mechanics

Transcription

1 Engineering Fracture Mechanics 78 (2011) Contents lists available at SciVerse ScienceDirect Engineering Fracture Mechanics journal homepage: Fracture and physical properties of carbon anodes for the aluminum reduction cell D.H. Andersen a,b, Z.L. Zhang a, a Norwegian University of Science and Technology, Department of Structural Engineering, NO-7491 Trondheim, Norway b Norsk Hydro, Primary Metal Technology, NO-6882 Øvre Årdal, Norway article info abstract Article history: Received 10 April 2011 Received in revised form 8 August 2011 Accepted 20 August 2011 Keywords: Carbon Anodes Aluminum reduction cell Fracture toughness Experimental study Cracks An experimental study with total 504 specimens has been carried out to investigate the fracture and physical properties of the carbon anode materials. The specimens were sampled from anodes produced with machined stub holes. From normal-and Weibull analysis the fracture toughness and the tensile strength showed a clear temperature dependency and orthotropic behavior. It has been found that both the fracture toughness and tensile strength increases with the temperature and are larger for the specimens directed in the horizontal direction than in the vertical direction. The variation in the tensile strength within an anode decreased with the temperature but the variation in the fracture strain increased. The tensile strain appears to be only dependent on the temperature and insensitive to the routine anode properties of the anode material. A multivariate linear regression analyses of the fracture toughness and tensile strength has been conducted and a typical correlation of R 2 = 0.5 (R is the Coefficient of Determination) to the measured routine anode properties was found. The thermal expansion coefficient is also larger in the vertical anode direction which makes the crack initiation more sensitive to temperatures. The orthotropic studies also showed that the air permeability has a tendency to be larger in the horizontal direction in the upper part of the anode which can induce unnecessary burning from the anode sides. The influence of the processing parameters in the paste plant and baking furnace has not been presented in this paper. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The anode s carbon material consists mainly of the raw materials of petroleum coke and coal tar pitch. The viscous coal tar pitch acts as a binder for the dry aggregate of the coke particles. In the production of the anode, the materials are mixed, compressed by vibroforming, and baked in large refractory furnaces at 1200 C to carbonize and solidify the compressed mixture and make it ready for electrolysis as a baked anode. The evaporation and carbonization of the pitch in the baking process is the main source of the porosity in the baked anode [1]. The carbonization of the pitch causes also volume shrinkage of the pitch and the entire anode. If the adhesion between the pitch and coke is poor, a greater part of interfacial pores are created compared to the pore content within the carbonized pitch. In addition to the pores in the carbonized pitch and the interfacial pores, there exist also pores within the petroleum coke particle. Good mixing, with finer coke particles and pitch filling the coke pores, can reduce the total porosity of the anode. The porosity is normally around 23 25% for vibroformed anodes [3]. The pore distribution in the anode is also non homogenous due to effects as particle segregation in silos and moulds, unstable fine fraction of coke particles and unstable sieving characteristics of the fine fraction. All these effects Corresponding author. address: zhiliang.zhang@ntnu.no (Z.L. Zhang) /$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi: /j.engfracmech

2 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Nomenclature Symbol description C1 the specimen for compressive- thermal- and electrical tests C2 the specimen for tensile tests C3 the specimen for three-point bending test A1 A7 anode numbers 1 7 collected from the anode production line. The specimens were sampled from these anodes T part the upper half of the anode (top part) B part the lower half part of the anode (bottom part) R Coefficient of Determination (from regression analysis) a Weibull scale parameter (peak position of the probability density bell shaped function) b Weibull shape parameter (controls the bandwidth of the probability density function) q baked anode density. specific electrical resistivity (SER) g air permeability r c cold compressive strength (CCS) E c Young s modulus of compression CTE thermal expansion coefficient k thermal conductivity e f fracture strain r t tensile strength E t Young s modulus of tension fracture toughness (mode I) by critical stress intensity factor K Ic can also contribute to local under pitching or over pitching in the anodes (or from anode to anode) and thereby create an unnecessarily high reject rate of baked anodes with cracks. The mechanical strength of the carbon anode is important in the production of aluminum. When the cold anode is set into the 960 C hot bath in the aluminum reduction cell it experiences a thermal shock. The temperature gradients together with the different thermal expansion coefficients of steel, carbon and cast iron combine to create crack driving forces in the anode. If the anode has too low crack resistance compared to the driving forces, anode material can fall into the bath and cause severe operational problems in the electrolysis cell. Furthermore, after days in the cell the partially consumed anode, the so-called anode butt, is taken out to be exchanged with a new anode. The anode butts are cleaned of the alkali and fluoriderich bath and prepared for recycling. Also in this process the mechanical strength of the anode is important as butts that cracked are harder to clean properly for electrolysis bath, and the extra impurities follow the material when it is recycled into new anodes. Usually butts make up 20 30% of the anode aggregate. The main effect of unwanted bath contamination is higher sodium impurities, which will increase the carboxy reactivity of the anode in the reduction cell. High carboxy reactivity anodes are unwanted since this causes unnecessary anode consumption, higher carbon dusting, reduced current efficiency and increased electrical resistance in the bath. The anode resistance to cracks is therefore very important when the aluminum reduction cell has to run effectively with high metal capacity and low operational costs. There are many possible methods to measure the fracture resistance parameter [2], but all have in common that a milled crack is defined when machining the test sample geometry. But the porosity in the anode material and pre-existing cracks from the production of the anode act as a source of scatter for the measurement of the fracture resistance parameter. This scattering demands a minimum number of samples due to evaluate the average value of the fracture parameter and to correlate it to routine measurements of the anode. In this study, both fracture mechanics tests and tension/compression tests have been carried out to determine the fracture toughness and other physical parameters. The fracture toughness is measured by the critical stress intensity factor, K Ic, based upon three-point bending tests (C3 specimens). The other mechanical properties are determined from tension tests (C2 specimens) and compression tests (C1 specimens). Table 1 shows the physical parameters found from each specimen type. The testing and analysis of the specimens are divided into three main studies: Determine the fracture toughness and the tensile parameters (C2) of the anodes, at different temperatures ranging from room temperature to 400 C. The values are presented with both Weibull and normal statistics. Study the correlation in the fracture toughness and tensile strength to the routine anode properties from the C1 specimen, since this is the standard laboratory specimen type used in the aluminum industry. Normally laboratories are sampling from around 1% of the anodes produced by the C1 type. Multiple linear regression analysis was used to fit routine anode properties (C1) to C2 and C3 parameters. Understand the orthotropic characteristics of the fracture toughness and the tensile parameters (C2) in the anode (vertical and horizontal anode directions)

3 3000 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Table 1 Physical parameters from three different specimen types; C1 is the specimen for compression, C2 the specimen of tension tests and C3 is the specimen of three point bending tests. Specimen type Parameter Symbol Unit C1 Baked density q kg/dm 3 C1 specific electrical resistivity. lx m C1 Air permeability g npm C1 Cold compressive strength r c MPa C1 Young s modulus (Compression) E c MPa C1 Coefficient of thermal expansion CTE 1/K C1 Thermal conductivity k W/mK C2 Fracture strain e f % C2 Tensile strength r t MPa C2 Young s modulus (tension) E t MPa p C3 Fracture toughness (Mode I) by critical stress intensity factor K Ic MPa ffiffiffiffiffi m Seven baked anodes (A1 A7) were sampled from the production line at Årdal Carbon in a period where the plant had a high scrap rate due to cracks in the baked anodes (autumn of 2008). Each anode was divided in twelve parts (six bottom parts, P1B P6B and six top parts, P1T P6T), and from each part six specimens were drilled, three horizontal (C1H, C2H C3H) and three vertical (C1V, C2V, C3V) as shown in Fig. 1. This gave a total of 3 specimen types 2 directions 12 anode parts 7 anodes = 504 specimens. In the experiment of Eliassen [4] the C2 and C3 parameters measurements of tensile fracture strain showed no correlation with temperature variation. However from the tensile experiments Ambenne [5] it was concluded that both the tensile strength and the Young s modulus of tension vary with the temperature and also it could be correlated to general C1 data. Meier [1] developed a thermal shock resistance (TSR) indicator for the anode where the variation of fracture energy (by the Weibull shape parameter or the Weibull modulus), was one of the parameters in the expression of the TSR. The variation of the fracture energy was found from a number of test samples from an anode. From the experiments (no orthotropic study) it was concluded that this parameter had the greatest influence on the TSR of the anode. Fig. 1. The positions of vertical and horizontal specimens in the anodes. The dimensions are in [cm]. The anode is seen from above for the upper drawing, and seen from the anode side for the lower drawing. The specimens are identified with anode number, anode part, specimen type and direction. For example, A1 P2B C3V is a vertical type C3 specimen in the bottom part 2 of anode 1.

4 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Specimen design 2.1. C1 specimen The C1 specimen is a cylindrical specimen with diameter of 50 mm. It is further divided into 20 mm- 76 mm- and 120 mm specimens as shown in Fig. 2 (note that the outer 20 mm part of each C1 specimen was discarded to avoid surface effects). The 20 mm specimen is used for thermal conductivity (k) measurements, and the 76 mm specimen is used for the thermal expansion coefficient (CTE) measurements using a smaller 20 mm diameter specimen drilled from this specimen. The permeability to air and the volumetric density are measured both by the 76 mm- and the 120 mm specimens. The preparation of the specimens and the methods for measuring the C1-parameters (Table 1) are standard practice [6,7] for the laboratory at Hydro Aluminum Årdal in Norway. The relevant ISO documents for the determination and preparation of the C1 parameters are given in [8]. The relevant ISO methods for each C1 parameter are documented in [9 14]. The thermal conductivity is determined by an R&D Carbon apparatus based on ISO [15]. All the C1 parameters were measured at the laboratory in Årdal. As a remark, the Young s modulus of compression from the laboratory in Årdal is measured far greater than its relative ISO method. In the Hydro method a modulus is being calculated from the total length of the sample. This modulus will be measured lower than a modulus found from a center part of the specimen. The modulus for the total length is therefore multiplied by a factor of 1.55 to equalize it with the modulus found from central parts of the specimen (research conducted by Kinston Research Centre by Alcan and Hydro). The reason is that the gripping plates will inhibit cracks and a greater contraction at both ends will arise during testing. As a result of these end effects the measured relative contraction will be larger when the total sample length is used than in the case where contraction is only measured along the center part C2 specimen The C2 specimen was designed for measuring the tensile properties. Eliassen [4] performed a finite element analysis to determine the optimum design of specimens for the tensile testing because earlier experiments with carbon materials had Fig. 2. The cylindrical C1 specimen, divided in a 20 mm, 76 mm and a 120 mm specimen. The positions of the different specimens in the anode are shown in Fig. 1. The dimensions are specified in [mm].

5 3002 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) shown that a large number of the test specimens fractured, not in the gauge area, but in the transition area of the specimen as shown in Fig. 3. Specimens with gauge diameters from 45 mm- to 55 mm and threaded ends of 80 mm were studied and it was found that the stress concentration in the transition area was improved by increased transition height. From the finite element analysis an initial transition height of 25 mm was chosen. The experiments with this transition height still result in some tests where the fracture appeared in the transition area instead of the gauge area. It was therefore decided to increase the transition height from 25 to 29 mm for the C2 specimen C3 specimen A mode I three-point bending specimen has been used to determine the critical stress intensity factor. Fig. 4 shows the design for the C3 specimen used in the experiments. The notch (a 0 from Fig. 4) needs to be large enough to obtain a certain amount of crack growth. The span, S, between the bottom rollers (Fig. 5) in the apparatus was reduced from 400 to 280 mm compared to Eliassen [4] to achieve a specimen less than half of the anode height. Fig. 3. The design of the C2 specimen for the tensile measurements. Fig. 4. The dimensions of the C3 specimen for measuring the critical stress intensity factor. The left plot shows a cross section where the initial crack is placed. The right plot is the specimen seen from the long side of the specimen. The z-direction is from bottom to top in the anode, and the y-direction is from left to right in the anode shown in Fig. 1.

6 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Fig. 5. Left main photo shows the experimental setup of the C2 specimen and right main photo the setup of the C3 specimen at ambient temperature. The miniature photos for the C2 specimen show the specimen both before and after the tensile test which induced the crack in the gauge area. The C3 specimen was visually the same before and after the maximum force was applied. Two MTS extensometers (type 634 3F-25) were placed on the opposite side of the C2 specimen in the gauge area. The bottom rollers for the C3 specimen define the span, S (Fig. 3). Both setups use the same DARTEC loader with compression for the C3 specimen and with tension on the upper steel nut (M80) of the C2 specimen (the lower M80 steel nut is fixed to the table). The DARTEC loader and the MTS sensors were both controlled and calibrated by the INSTRON controller 8800 using the control Software, Bluehill ver The critical intensity factor can be calculated from handbooks for the most common specimens [16]. 3. Setups The experimental setup for the parameters of the C1 specimen is described in [6] and in the relevant ISO documents [8] Room temperature setup of the C2 and the C3 specimen The left photos in Fig. 5 show the apparatus used in the tension tests of the C2 specimens. A loader, with a 50 kn load cell, was used to apply the tensile force. Displacement-controlled loading with a constant displacement rate of 1 mm/min is applied. The load displacement curve was recorded and the load was continued until the specimen fractured. The two extensometers measured the elongation in the gauge area of the specimen. A pair of steel nuts (M80) is screwed into the tension specimen ends (see also Fig. 3). The elongation, force and displacement of the load cell were recorded through the loading process. Two extensometers were used in the ambient temperature tests, placed opposite and parallel to each other. This will decrease the error in measuring due to the bending moment. The gauge length of the extensometer was 55 mm. The strength of the material was calculated according to the following equation [17]: r t ¼ P max A gage ð1þ where P max, is the measured maximum load and A gage the cross section of the nominal gauge area. To determine the Young s modulus, E t, the measured stress versus strain curve was used (measured average engineering strain from the MTS extensometers). The Young s modulus is the tangent to the linear part of the curve, where the material follows the Hooke s law. The modulus was automatically found by the software using slack correction functionality; a procedure which analyzes the slope of the stress strain curve and determines the correction at the point where the modulus line intersects the zero-stress strain axis. The fracture strain, e f, was found as the engineering strain where the maximum tensile stress was obtained and the specimen failed. Fig. 6 shows a screen shot of the measured stress strain curve from the Bluehill software for the tensile test, A5- P1B-C2H, with slack correction (common initiation for the curves). The discontinuous point on the curves is where the C2 specimen fractures.

7 3004 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Fig. 6. A screen shot of the measured stress strain curve from the tensile test of specimen, A5 P1B C2H. Fracture occurs at the discontinuous point on the curve. For the C3 specimen, the software was configured for a three- point-bending test. The load was applied at the position of the initial crack as the right photos in Fig. 5 shows. The maximum applied load from the load-defection curve was set into equation 2 as F Q for computation of the critical stress intensity factor of Mode I, which is the British Standard BS7448 [16] for determination of K Ic. Fig. 7 shows a screen shot of a typical load deflection curve from the control software K Q ¼ F QS BW f a ð2þ 1:5 W h a 3 a 0:5 1:99 a W W 1 a W ð2:15 3:93 a þ 2:7 i a 2 Þ W W f ¼ W 21þ2 a W 1 a 1:5 ð3þ W p The calculated toughness values are found setting S ¼ 0:28 m; W ¼ 0:1m; a=w ¼ 0:5; B ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:06 m 0:05 m as shown in Fig. 4 (the C3 specimen has two different values of the width; B N = 0.05 m in the fracture area and B = 0.06 m elsewhere). For a specific specimen, numerical analysis could be used to determine a normalized factor, f, valid for crack lengths over a larger range than described in [16]. Eliassen [4] made such analysis and showed that Eq. (3) and the expression from the finite element analysis gave the same values for larger crack lengths; hence Eqs. (2) and (3) are used to determine the toughness values for the C3 specimens Temperature setup Tests that were conducted in the heat chamber furnace were run slightly different from the room temperature tests. The chamber, as shown in Fig. 8, was heated to 200 C for all the C2- and C3 specimens from the A2 anode, and to 400 C for all Fig. 7. Screen shot of the load deflection curve for the three-point bend test of the C3 specimen, A5 P6T C3H. The maximum load for each specimen is the value used in equation 2 and 3 for computing the toughness value. Each specimen is identified with a code as described in Fig. 1.

8 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Fig. 8. Left photo shows the experimental setup of the C2 specimen and right photo the setup of the C3 specimen for the temperature tests. The C2 specimen is shown after fracture. An extensometer, coated with ceramics and protected by water cooling was placed in the gauge area of the C2 specimen. Both specimen types were placed into a DARTEC heat chamber. The temperature of the heat chamber was controlled by two temperature measurements; one thermo element drilled 3 cm into the anode material (example shown on the right photo where the element is drilled into the H ), the other is a built in temperature sensor for the DARTEC chamber which measures the temperature in the chamber. The measurements of the specimens were performed when both temperatures were within ±5 C of the temperature reference. The temperature reference was set to 200 C for all the C2- and C3 specimens from the A2 anode, and set to 400 C for all the C2- and C3 specimens from the A3 anode. the C2- and C3 specimens from the A3 anode. The gauge length of the extensometer was 25 mm. The extensometer was also cooled by water at a constant flow rate. 4. Results and discussions All the 504 specimens from the seven anodes (A1 A7) were tested in a 5 week s period. The anodes A1, A2 and A3 were positioned beside each other in the baking furnace at Årdal Carbon. A2 and A3 were also produced subsequently in the paste plant. A4 and anode A7 contained distributed visible vertical cracks of greater than one centimeter length. These two anodes are therefore not presented in the following plots, but only in the tables. All the anodes were produced by petroleum cokes from the coke suppliers, CII and Statoil with a blend of 75% CII and 25% Statoil. The stub holes of the Årdal anodes are made by drilling after the anode has been baked. This is unlike other anode plants where the holes are formed during compression of the anode paste in the vibrocompactor. It is therefore expected that the anode top is more homogeneous than the typical anodes produced worldwide. All the analyses were performed with the statistical toolbox in Matlab 2009b (software from the company, MathWorks, 3 Apple Hill Drive Natick, Massachusetts 01760, USA) Temperature dependent tension- and fracture properties of the anode Meier [1] emphasized that the distribution of the flexural strength of the anode can be characterized very well with Weibull statistics. The variation of the flexural strength was quantified with the Weibull shape parameter, b. From his extensive experiments with anodes, Meier categorized the anode quality after the value of the Weibull shape parameter: b 3 which indicated a high variation in flexural strength, given as a wide bell shaped distribution and also representing poor anode quality, b 10 indicated a medium variation with typical anode quality, and b 13 resulted in little variation and a narrow bell-shaped distribution, representing high anode quality. Meier concluded from this work that anode cracking can be avoided more efficiently by decreasing the variation rather than improving the average anode quality. It should be noted that the shape parameter will generally be lowered if both horizontal- and vertical specimens are used in the same statistics and increased if only one of the directions is used for the analyses. The reason is that the vertical- and the horizontal specimens have different average values of fracture- and tension properties as will be discussed below. Munz and Fett [18] derived the relation between the distribution and the maximum flaw size and the strength of the material. Their work was based on the assumption that the largest flaws are responsible for failures, and that a failure occurs when the weakest link breaks. There will be a higher probability of finding a weaker link when a greater volume of material is analyzed. This means that there will statistically be found a lower strength, r tot, if the whole anode is examined, compared to the lowest strength, r specimens, found if only some specimens from the anode is examined. The ratio of strengths r tot / r specimens due to the volume size effect, V specimens /V tot, is given by Weibull [19] and shown in the following equation

9 3006 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) r tot r specimens ¼ V 1 b specimens ð4þ V tot As an example, assume the specimens examined are 0.1% of the total volume that could have been examined and the Weibull shape parameter is b = 10 from the specimens. Then the lowest strength that could have been found if the total material had been examined, is only a half of what is found in the analysis of the specimens ( = 0.5). Eq. (4) emphasizes how important it is to reduce the variation of the anode strength by increasing b. From the analyses the average tensile strength of the C2 specimen was determined from seven anodes (A1 A7). Table 2 shows that the Weibull shape parameter for A4 and A7 had values of b around 3 for the tensile strength, the same order as Meier [1] defined as poor anode quality. The A4 and A7 anodes were also observed with visual vertical cracks for a larger number of specimens. The other ambient temperature anode measurements (A1, A5, A6) gave b 10 for the tensile strength (typical anode quality, the number would probably have been larger if specimens from only one direction had been analyzed). But for the high temperature measurements (A2 at 200 C and A3 at 400 C it is clearly seen that the Weibull shape parameter, b, increases with the temperature, from b = 10 at ambient temperature to 17.0 at 200 C and to 20.4 at 400 C. This is a surprising observation since it was expected that the temperature measurements would suffer from more noise in the data due to more handling of the specimens in the heat chamber. The narrower bell shaped distribution of tensile strength for higher temperatures are shown in Fig. 9, 1st column, 2nd row of plots. The peak of the density curves is given by the Weibull scale parameter, a, and is the mean value for the Weibull distribution. Narrower bell shaped distributions at higher temperatures for the tensile strength improved the correlation between temperature and tensile strength in the measurements; the 5% probability limit of the tensile strength of the A3 anode (400 C) is just below the 95% probability limit of the tensile strength of the A2 anode (200 C), and the 5% probability limit of the A2 anode is just below the 95% probability limit of the ambient temperature anodes (Table 2 and 2nd column, 2nd row of plots, Fig. 9). Table 2 Weibull- and normal statistics of the parameters from the C2- and C3 specimens. Physical property Anode ID Mean STD Weibull Scale parameter a Weibull Shape parameter b 5% probability Weibull limit 95% probability Weibull limit Fracture toughness ðmpa ffiffiffiffiffi A p m Þ A (200 C) A (400 C) A A A A Tensile strength A (MPa) A (200 C) A (400 C) A A A A Fracture strain (%) A A (200 C) A (400 C) A A A A Young s modulus A (tension) (MPa) A (200 C) A (400 C) A A A A Nr. of samples

10 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Fig. 9. Left plots: The Weibull Probability Density function (named Density in the plots). Right plots: Cumulative Probability function of the tension- and fracture properties of anode A1, A2, A3, A5 and A6 from the C2- and C3 specimens. There is a maximum of 24 measured samples for each curve (12 horizontal specimens and 12 vertical specimens of the same specimen type in each anode). See Table 2 for further statistical information. The A2 anode is tested at 200 C, the A3 anode at 400 C and the other anodes are at room temperature. The decrease of the variation in strength with the temperature will make the variation in toughness closer to the variation in fracture strain. This can be seen in Fig. 9 where the variation in the toughness and fracture strain experience almost the same amount of increase (b is reduced by around 40% up to 400 C), even they are measured by different specimen types. The ambient temperature anodes (A1, A5, A6 in 1st column, 2nd row plot in Fig. 9) has different mean tensile strengths, with A5 having the largest strength and A1 the lowest. But the distribution of the fracture strain for these three anodes was almost the same (1st column, 3rd row, Fig. 9) despite the fact that they have different baked densities (C1 parameters in Table 3). The fracture strains were surprisingly insensitive to the differences in C1 properties but only dependent on temperatures (1st column, 3rd row plot in Fig. 9). With the same fracture strain, the measured Young s modulus of tension will

11 3008 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Fig. 9 (continued) Table 3 Weibull- and normal statistics of the parameters from the C1 specimens (routine anode properties). All the C1 specimens are analyzed at room temperature. Physical Property Anode ID Mean STD Weibull scale parameter a Weibull shape parameter b Nr. of samples Baked Density (10 3 kg/m 3 ) A A A A A A A Cold compressive strength (MPa) A A A A A A A Young s modulus (compression) (MPa) A A2 10, , A3 10, , A4 10, , A5 10, , A6 10, , A Coefficient of thermal expansion (1/K) A A A A A A A Specific electrical resistivity (lx m) A A A A A A A Thermal conductivity (W/mK) A A A A A A A

12 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) probably correlate in a higher degree to the measured tensile strength ðr ¼ E e Þ; Young s modulus, as the tensile strength, is the largest for the A5 and the lowest for the A1 anode (among A1, A5, A6 shown in 1st column, 4th row plot in Fig. 9). While the tensile strength shows a reduced variation with the increase of temperature, the variation of fracture strain increases with the temperature. The b value of the tensile strength of anode, A1, A5 and A6 reduce from over 7 at room temperature to 5.9 for A2 and to 4.5 for A3 at 400 C. The variation in the tensile strengths and fracture strains for different temperatures are illustrated in Fig. 10. The rectangles in Fig. 10 cover the range within 5% and 95 % of the Weibull probability limits of tensile strength and fracture strain. The lines are drawn with the 5% and 95% Weibull probability slopes (Young s modulus). In the experiments, all the room temperature fracture strains were average values of two measurements (from two extensometers at the specimen). The high temperature measurements had only one extensometer, and the strain is from a single measurement, causing a larger variance in the fracture strain. It is therefore assumed that the real probability density functions of A2 and A3 has a narrower bell shape (larger b) for the fracture strain and the Young s modulus than what is shown in Fig. 9, 1st column, 3rd and 4th row. This means that the Young s modulus will probably have a better correlation to temperature than what is measured. However, the measurements still shows that the Young s modulus decreases with temperature, from an average around 8500 MPa at ambient, to 7100 MPa at 200 C, and 6800 MPa at 400 C (referring to the Weibull scale parameter in Table 2). Among the anodes tested at room temperature (A1, A5, A6), the A5 anode has the largest fracture toughness (1st column, 1st row, Fig. 9), and A1 the lowest. This observation is the same as for the tensile strength (1st column, 2nd row) and the Young s modulus of tension (1st column, 4th row). The fracture toughness increases with the temperature, as the tensile p strength does, from averages of 1:42 MPa ffiffiffiffiffi pffiffiffiffiffi pffiffiffiffiffi m at ambient temperature to 1:59 MPa m for A2 at 200 C and 1:67 MPa m for A3 at 400 C (Weibull scale value in Table 2). Among the room temperature anodes, A5 can be ranked as the best with the largest fracture toughness and tensile strength, then the A6 anode, and at last the A1 anode (with exception of the A4 and A7 anode which was regarded as crack anodes). From the routine anode properties shown in Fig. 11, this ranking is only found in the Young s modulus of compression. No other routine anode properties from the C1 specimens follow this ranking Orthotropic properties of the anode One way of characterizing isotropic and anisotropic petroleum coke is by computer based image analysis, using a microscope where the Pore Axial Ratio is measured (pore breadth width divided by longest pore diameter where the breadth is the widest point perpendicular to the longest diameter). Hume [20] found that isotropic cokes have a typical axial ratio of 0.6, while anisotropic cokes have axial ratios around 0.3. Coke shipments will be a mixture of isotropic and anisotropic coke and will have different axial ratios. Normally, there is no quality control in the aluminum industry for the isotropy of a coke shipment, and the value is therefore not known for the anodes, A1 A7. In any case, since the axial ratio is lower than 1.0, the anode will have orthotropic properties. In the forming process, the paste is compacted by vibration and a great part of the particles will orient horizontally. In addition to the particle orientation, this effect can be amplified with creation of interfacial pores in the baking furnace. Interfacial pores depend on the adhesion between the binder pitch and the coke filler, and Fig. 10. Stress strain curve for the three anodes, A1, A2 and A3. The rectangles cover the area within the 5% and 95% Weibull probability limits of the fracture strain and the tensile strength (Table 1). The height of the rectangle is reduced by higher temperature and the width of the rectangle is increased by higher temperature, meaning that the variation of the tensile strength is reduced by increased temperature and the variation of the fracture strain increases by increased temperature from the measurements. The two green lines show the 5% and 95% Weibull probability slopes (Young s modulus) of the room temperature anode, A1, the orange lines (5% and 95% probability slopes) for the A2 anode, and the red lines for the A3 anode.

13 3010 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Fig. 11. Weibull Probability Density functions for the routine anode properties of the C1 specimens (named Density in the plots). There is a maximum of 24 measured samples for each curve (12 horizontal specimens and 12 vertical specimens of the same specimen type in each anode). See Table 3 for further statistical information. All the C1 specimens were tested at ambient temperature (also for specimens from A2 and A3). the extent to which this is maintained when the binder pitch shrinks during the anode baking heat treatment. The binder phase will shrink during carbonization due to loss of volatiles and growth of the graphitic crystallite lattice. If adhesion is poor, the binder phase may separate during the carbonization, opening up interfacial pores. If adhesion is maintained, then the contraction of the matrix may pull the grain and an overall shrinkage of the anode ensues. Even if interfacial pores are being created, a total anode expansion (rather than shrinkage) can occur if the internal pressure of the gaseous pitch volatiles inside the anode is too large. This can happen if the heat-up curve is steep. Anode A5 was chosen for the study of orthotropic characterization of the anode. This anode contained less noise from coke segregations and cracks. It had the lowest standard deviation in the baked density and the electrical resistivity (Table 3). At the same time, all the paste within one anode has experienced the same set point settings of control parameters from

14 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) the production line. In addition there are no specimens missing for A5. Fig. 12 shows the orthotropic character of A5 for all the parameters measured from the C1, C2 and C3 specimens (Fig. 12 has 2 columns and 6 rows of plots for a specific parameter). Seven of the eleven physical parameters in Fig. 12 show a clear orthotropic property (these are further described in Fig. 13 and Table 4). From the routine anode properties (C1 parameters) the following four parameters show an orthotropic effect: Fig. 12. Surface plots of 11 anode properties for the A5 anode. The upper coordinate system for a physical parameter shows the top part, T, of the anode and the lower coordinate system shows the bottom parts, B, of the anode. In each coordinate system there are two surfaces, one with mesh lines and one without. The surface with mesh lines shows measurements from vertical specimens, and the surface without mesh lines measurements from horizontal specimens. Each surface is interpolated from 6 specimen measurements, but not extrapolated. The different coordinate systems have different view angels in order to see as much as possible of the two surfaces.

15 3012 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Fig. 12 (continued) (1) E c, Young s modulus of compression (1st column, 6th row of plots, Fig. 12), (2) k, Thermal conductivity (1st column, 4th row, Fig. 12), (3) CTE, Coefficient of thermal expansion (2nd column, 4th row, Fig. 12) and (4)., specific electrical resistivity (1st column, 5th row, Fig. 12). Using the Weibull scale parameter, a (Table 4 and Fig. 13) these four parameters have horizontal averages greater by: 11.2% (Y t ), 7.3% ðkþ, and less by 3.8% (CTE) and 4.0% (.) compared to their corresponding vertical averages. For the tensile- and fracture parameters (C2- and C3 parameters), the fracture toughness, tensile strength and Young s modulus of tension were 9.5%, 11.8% and 14.0% greater than their corresponding vertical averages, measured by the Weibull Scale parameter, a in Fig. 13 and Table 4.

16 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) Fig. 13. Weibull Probability Density function (left) and the cumulative probability function (right) of the ratio of horizontal/vertical measurements of seven parameters from the A5 anode. Each curve is found from 12 horizontal/vertical value pairs in the A5 anode. Table 4 Weibull- and normal statistics of the ratio of Horizontal/Vertical value pairs in anode, A5, for the seven parameters that are sensitive to orthotropic behavior of the anode. Ratio of physical properties (horizontal/vertical specimen values of A5 anode) Mean STD Weibull scale parameter a Weibull shape parameter b 5% 95% Nr. of samples FRACTURETOUGHNESS pairs Tensile strength pairs Y modulus (tension) pairs Y modulus (compression) pairs Electrical resistivity pairs Therm. conductivity pairs Coefficient of thermal expansion pairs Baked density pairs An increased thermal shock resistance for the anode demands higher fracture toughness and a lower CTE. Given the orthotropy measured, the thermal shock resistance to the vertical cracks is better compared to horizontal cracks. Vertical fracture driving forces to Mode I horizontal cracks are clearly more dangerous, given that the fracture toughness is lower. As observed, the fracture strain was insensitive from anode to anode (A1, A5, A6). It can also be seen that the fracture strain is more or less insensitive to directions inside the anode (1st column, 3rd row, Fig. 12). As discussed earlier, Young s modulus of compression was the only routine parameter which ranked A1, A5 and A6 the same way as the fracture- and tensile parameters. This routine parameter is also the most sensitive to orthotropic behavior inside the A5 anode. Many aluminum plants run projects to increase the electric current to increase the metal production. Often the anode length is increased to allow increased current and metal capacity. For many anode plants the length has passed 1600 mm and the risk of having different anode properties between the anode ends becomes higher. From Fig. 12, a U-profile surface (or inverted U-profile surface ) in the upper part of the anode for the horizontal specimens, is shown for the fracture toughness, baked density, compression strength, and electric resistivity (surface plot without mesh lines in the upper coordinate system in Fig. 12). But when we look at the upper horizontal plot for the air permeability, it has a decreasing value from left end to the right end of the anode, instead of the U profile (even if the baked density is higher at left end). Normally the density and the air permeability are strongly correlated, but since the measurements of the air permeability are mostly sensitive to macro pores (>10 lm), the correlation can be reduced if the mean pore size differs; even if the total pore volume is the same. From this viewpoint it seems that the pores are fewer and bigger in the upper left end and more and smaller in the upper right end (for the horizontal direction). Sadler [21] and Cutshall and Bullough [22] showed experimentally that internal carboxy attacks can be directly related to permeability. They found that the visible zone of surface oxidation was more significant on the side of the anode butts (upper part of anode). This is in accordance to the experiments which shows a larger horizontal than vertical permeability in the upper anode (horizontal surface plot, 2nd column, 3rd row of plots, Fig. 12). There can be different reasons for higher horizontal air permeability in the anode top: (1) In the forming process, the paste is compacted both from the top- and the bottom surface by two steel weights vibrating at Hz. The two weights vibrate near opposite phase to create a large compaction force. Due to the momentum of the 1000 kg anode weight the anode does not lift off the lower vibrating weight. It is the upper weight which

17 3014 D.H. Andersen, Z.L. Zhang / Engineering Fracture Mechanics 78 (2011) lifts off the anode paste between the strokes. This means that the peak amplitude of the vibrated signal of the upper weight is further away from the average amplitude (further away from a single frequency sine periodic function). The upper anode paste will therefore experience an input displacement signal which contains a larger spectrum of frequency components and thereby increase the possibility for larger particle orientation in the anode top. Since many of the pores in the anode are interfacial, these pores will also be created horizontally in the baking furnace. (2) A second explanation is segregation of particles so that the recipe for correct aggregate composition is not fulfilled locally. This reduction in the packing density will increase the volume of inter-particle voids when grains are oriented during the vibration. The increased gas volume increases the risk for higher horizontal permeability. The anodes for the experiment were sampled from production in a period with a comparatively higher rate of anodes with cracks. A program was initiated to decrease the cracking rate. By process-, technical-, and raw material actions the reject rate was reduced. Årdal Carbon has a milling machine for the anode stub holes and has the ability to define the anode top to be either parallel or normal to the vibration direction in the forming process, dependent on which problem the electrolysis plant is experiencing. Typical anode problems which can change by anode orthotropy in the electrolysis cell are carboxy reactivity induced dusting, horizontal- or vertical anode cracks or large electric power consumption for metal production. The orthotropic properties found from these anodes can change for different coke shipments since the isotropy of the coke is given by how the suppliers of the coke have mixed the different coke types. The orthotropic anode behavior can therefore be changed with the right blending of raw materials. For the future it is important to establish quality criteria for the coke isotropy which is valuable information for tuning different process control parameters in the mixing-, forming- and baking process of the anode. This tuning can amplify fracture toughness, electrical power loss and low reactivity rates to different optimal directions in the anode. It is important to be flexible both in the blending process of raw materials for tuning orthotropic behaviors, but also be flexible in the choice of defining the anode top in the normal- or parallel vibration direction in the forming process of anodes. The orientation of the anode in the baking furnace can also affect the orthotropic anode character. Since the electrolysis plants struggles in periods with different problems, either with high reactivity or high anode crack rates, the anode can be adjusted more easily to overcome such problems Correlation of tensile- and fracture properties to routine measurements In this section, the correlation of tensile- and fracture parameters to the routine anode properties (from C1) were studied. The baked density, q, strongly correlates to the other routine anode properties like permeability (g), specific electrical resistivity (.) and Young s modulus (E). Normally the electrical resistivity and the air permeability will decrease with higher density as long as no cracks appear in the anode production and the average porosity is not changed. For the anodes in these experiments, A4 and A7 are anodes with visual vertical cracks. They are also the anodes with the highest baked density, but not the lowest resistivity. The cracks from the production destroy these correlations. Many different linear regression fits were tried, but only one fit for the fracture toughness and the tensile strength is documented by this paper, as shown in the following equation K IC ¼ a 0 þ a 1 q þ a 2 g þ a 3. þ a 4 E c ð5aþ r t ¼ b 0 þ b 1 q þ b 2 g þ b 3. þ b 4 E c ð5bþ The a-coefficients were found for the fracture toughness (5a) and the b-coefficients for the tensile strength (5b). For a multivariate regression fit it is an advantage that the effect variables do not correlate with each other since this would hide each variables effect on the variation in the fracture toughness and tensile strength. Regression analysis of several combined variables like q g, q. and 1=q E c was also performed to study if a fit became better than what was found from Eq. (5) (Coefficient of Determination, R 2 0.5). No improvements of the fits were observed from such testing. The A5 anode was studied and the results are shown in Fig. 14 and Table 5. The multivariate fits of the tensile strength (lines in the right plot of Fig. 14) showed coefficients of determination, R 2 = {0.53,0.55,0.54} for the vertical direction, horizontal direction and for the total A5 anode (Table 5). The fits also show a larger value of the tensile strength in the horizontal direction. The coefficients of Determination are the almost the same for each direction (Table 5). But for the fracture toughness, the uncertainty of predication in the horizontal direction is high (R 2 = 0.22 from Table 5). This can be explained since the milled crack in the horizontal C3 specimen is parallel to the observed cracks made from the production of the anodes. The variation in the vertical crack propagation and the crack tip stress field are probably more exposed to random crack meandering and deflection due to the particle orientations (if intergranular propagation is assumed) and can introduce more noise in the measurements. To improve the fits in all directions for both the tensile strength and the fracture toughness, the dimensions widths of the C2 and C3 specimen could have been larger, but the volume of density measurements reduced. For example the density of the C2 specimen can be measured in the gauge area, and for the C3 specimen, a volume around the milled crack. If not the