Quantification of cyclic twinning-detwinning behavior during low-cycle fatigue of pure magnesium using high energy X-ray diffraction

International Journal of Fatigue 125 (2019) 314–323

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Quantification of cyclic twinning-detwinning behavior during low-cycle fatigue of pure magnesium using high energy X-ray diffraction

T

⁎

Aeriel D. Murphy-Leonarda, , Darren C. Paganb, Armand Beaudoinb, Matthew P. Millerc, John E. Allisona a

University of Michigan, Department of Materials Science and Engineering, Gerstacker Building, 2200 Bonisteel Blvd, Ann Arbor, MI 48109, United States Cornell High Energy Synchrotron Source, 277 Wilson Lab, Ithaca, NY 14853, United States c Cornell University, Sibley School of Mechanical and Aerospace Engineering, 407 Upson Hall, Ithaca, NY 14853, United States b

A R T I C LE I N FO

A B S T R A C T

Keywords: Low cycle fatigue Magnesium alloys Cyclic properties Synchrotron diffraction Twinning Detwinning

The cyclic twinning and detwinning behavior of extruded Mg was investigated using in-situ high energy X-ray diffraction (HEXD) under fully-reversed low cycle fatigue conditions. Measurements were conducted at three levels of applied strain. The initial texture was such that the c-axis in most grains was perpendicular to the loading direction, an orientation in which extension twinning is favored during compressive loading. At strain amplitudes greater than 0.5%, tension-compression asymmetry was observed during cyclic loading and related to cyclic twinning and detwinning. The twinning and detwinning behavior were characterized by monitoring the evolution of X-ray diffraction peaks associated with the basal {0 0 0 2} planes throughout selected cycle. At cyclic strains greater than 0.5%, in-situ HEXD results show that twinning occurs during the compression portion of the cycle and, at early stages of fatigue, most twins are detwinned under reversed loading during the tensile portion of the cycle. It was also observed that as the number of fatigue cycles increases the twin volume fraction increases. After 100–200 fatigue cycles, the detwinning process was observed to be incomplete and a significant fraction of residual twins remained throughout an entire cycle. Using electron back scatter diffraction imaging on the surface of interrupted fatigue tests, twinning and detwinning behavior was investigated and the presence of persistent twins, including residual twins, was observed. At a lower applied strain (0.4%), twinning and tension-compression yield asymmetries associated with twinning were not observed.

1. Introduction Mechanical twinning plays an important and well documented role during the plastic deformation of Mg and its alloys [1–8]. In most Mg alloys, basal 〈a〉 slip and twinning are the predominant modes of deformation, since prismatic 〈a〉 slip, pyramidal 〈a〉 slip, and pyramidal 〈c + a〉 slip require much higher stresses to activate during deformation [9]. Mechanical twinning eases deformation along the c-axis and helps Mg and its alloys satisfy the Von Mises Criterion for five independent deformation systems [9]. Due to its importance, extension twinning has been the focus of significant, active research [e.g.,10–20]. When loaded in compression parallel to the basal plane, extension twins can form causing an 86.3° reorientation of the basal pole [9,12,19]. During reversed (tensile) unloading these twinned regions can become narrower and/or disappear in a process known as detwinning [9,21–22]. Detwinning causes a reorientation of the c-axis from the

twin back to the matrix or parent grain [21–23]. Twins can reappear upon reloading and thus, the twinning-detwinning behavior continues until the end of life [24]. During low cycle fatigue (LCF) deformation of magnesium alloys, this cyclic twinning and detwinning behavior leads to a tension-compression strength asymmetry where the stresses in tension are usually higher than those in compression [4–5,12]. Begum et al. found that the tensile yield strength was much higher than the compressive yield strength during low cycle fatigue of an AM30 extruded Mg alloy and related the strength differences to twinning that occurs during compression and detwinning that occurs during tension [5]. A study by Yu et al. found that the tension-compression yield asymmetry was reduced at low strain amplitudes during LCF of pure polycrystalline magnesium due to a reduction in twinning [3]. Other studies have used neutron irradiation and synchrotron diffraction as well as electron back scatter diffraction (EBSD) to study the alternate occurrence of twinning and

⁎

Corresponding author. E-mail addresses: [email protected] (A.D. Murphy-Leonard), [email protected] (D.C. Pagan), [email protected] (M.P. Miller), [email protected] (J.E. Allison). https://doi.org/10.1016/j.ijfatigue.2019.04.011 Received 12 September 2018; Received in revised form 27 March 2019; Accepted 7 April 2019 Available online 08 April 2019 0142-1123/ © 2019 Published by Elsevier Ltd.

International Journal of Fatigue 125 (2019) 314–323

A.D. Murphy-Leonard, et al.

The samples were then prepared using standard metallographic techniques, finishing with a 0.05 μm polycrystalline diamond solution. Care was taken to minimize polishing-induced deformation twins. An aceticnitric solution (10 mL nitric acid, 5 mL acetic acid, 20 mL water, and 60 mL ethanol) was used to etch the specimens for 5 s, which revealed grains and twins under scanning electron microscopy. These samples were then subjected to cyclic deformation and periodically examined using EBSD with no further surface preparation. The flat sample geometry was consistent with the ASTM E606 standard and the samples had a thickness of 4 mm and a gage length of 12 mm.

detwinning during cyclic loading [11–12,25–30]. Wu et al. reported an abnormal sigmoidal shaped hysteresis loop during LCF of the Mg alloy AZ31, where the stress in tension was much higher than that in compression and related the observed behavior to twinning-detwinning using neutron scattering [25]. To date, no comprehensive studies of cyclic twinning and detwinning have been reported on unalloyed Mg, an important reference condition for quantitative understanding of alloying effects on cyclic stress-strain and LCF. In the current work, the cyclic twinning and detwinning behavior of extruded, polycrystalline, unalloyed magnesium under LCF loading was investigated at the Cornell High Energy Synchrotron Source (CHESS) using in-situ HEXD. The purpose of this study is to quantify the evolution of extension twins and the detwinning behavior that occurs during cyclic deformation and to understand the influence of twinning and detwinning on cyclic stress-strain response of pure Mg. This quantitative information will provide important baseline information for the broader goal of developing physically-based models for incorporation into crystal-plasticity finite element models for predicting the influence of microstructure and alloying on cyclic stress-strain response and low cycle fatigue [31].

2.2. Cyclic loading and X-ray diffraction measurements HEXD experiments were performed during in-situ cyclic mechanical loading at the F2 Station at the Cornell High Energy Synchrotron Source (CHESS). Fig. 2 shows an illustration of the experimental geometry which will be referred to throughout this section. Within the diffraction volume, every grain satisfying Bragg’s Law (Eq. (1)) will diffract producing a peak of diffracted intensity on the detector. Bragg’s Law relates the X-ray wavelength, λ to the lattice spacing for a unique family of planes, dhkl and the diffracted angle, θhkl [34].

2. Experimental procedure

(1)

λ = 2dhkl sinθhkl

2.1. Material characteristics and sample preparation

The cyclic loads were applied by a Bose Electroforce 3200 Series III load frame that was mounted on a series of translation and rotation stages for sample manipulation. The macroscopic load was measured on a 5 kN load cell located below the sample. The macroscopic strain was measured using an extensometer attached to the sample. Two samples per condition were tested at both 0.52% and 0.75% total strain amplitudes while only one sample was tested at 0.4% total strain amplitude. During the test, the sample was illuminated by a 61.332 keV X-ray beam that aligned parallel to the -Z direction. The size of the beam illuminating the sample was 1.25 mm (width, X) by 1.25 mm (height, Y). Diffracted intensity was measured in transmission on a wide panel area amorphous silicon detector that was placed with face normal to the incoming beam, 859 mm behind the specimen. A sufficient number of grains were illuminated such that nearly complete Debye-Scherer powder rings were captured on the detector. To maximize the number of crystals illuminated, the sample was continuously rocked about the rotation axis, ω, from 0 to 5°. The timing of the rocking was synced such that a rotation from 0° to 5° and back to 0° degrees was completed during a single exposure. Diffracted intensity was measured at an angle 2θ from the incoming X-ray beam and the angle η defined the azimuthal position along the Debye-Scherer ring at which the diffracted intensity was measured which was 5°. The area detector employed was a GE41RT+ amorphous silicon area with 2048 × 2048 pixels and 200 µm × 200 µm pixel size. The cyclic loading was performed in displacement control with displacement end points. A triangular displacement waveform was applied to the specimens. Three different specimens were tested with displacement endpoints of 0.205 mm (εA = 0.75%), 0.192 mm (εA = 0.52%), and 0.135 mm (εA = 0.4%). When not collecting diffraction data, the sample was loaded at a frequency of 0.25 Hz. The loading direction was perpendicular to the incoming X-ray beam. In this geometry, the poles of diffracting lattice planes lie at an angle, θ, away from the loading axis. To observe the twinning process in-situ, a cycle was applied to the specimen and diffraction measurements were continuously made throughout the cycle. During these cycles, the loading

The unalloyed Mg used in this study was provided by CanmetMATERIALS, in the form of extruded bar. The composition of the extruded material was determined by the Center of Materials and Sensor Characterization using inductively plasma mass spectrometry and is listed in Table 1. The bar was extruded from an 85 mm diameter cast billet at 300 °C to a final diameter of 15 mm. The as-extruded texture was measured using EBSD with the results shown in Fig. 1. In the in-situ loading experiment described below, samples were machined such that the loading direction was parallel to the extrusion direction. It should be noted that the extrusion direction is oriented out of the page. The initial texture was such that the basal poles are oriented normal to the extrusion direction and the loading direction [32]. The microstructure consisted of equiaxed grains with an average grain diameter of 50 μm. The microstructure was 95 percent recrystallized. The details of this microstructural characterization have been reported elsewhere [33]. For the in-situ synchrotron diffraction experiments, cylindrical fatigue specimens were machined by Westmoreland Mechanical Testing and Research, Inc. (WMTR) using low stress turning to ensure a low residual stress, scratch free surface. The final surface was prepared by standard metallographic techniques ending with a 1200 μm grit finish. The geometry was consistent with the ASTM E606 standard and the samples had a diameter of 6.35 mm and a gage length of 19.05 mm. Twinning and detwinning were also characterized using electron back scatter diffraction (EBSD) on the surface of flat, rectangular fatigue specimens inserted in a Tescan Mira 3 scanning electron microscope equipped with an EDAX Hikari XP EBSD detector. Each EBSD scan was taken at a voltage of 30 kV and a beam intensity between 18 and 20 with an average step size of 1.0 ± 0.2 μm. TSL OIM software was used to characterize EBSD data and an average confidence index of 0.67 ± 0.1 was obtained. No additional confidence index cleaning was applied to the data. A grain tolerance angle of 5° was used for grain recognition. These were also machined by WMTR using low stress grinding where the final surface was produced with 1200 μm grit finish. Table 1 Chemical composition of unalloyed Mg. Element

Na

Al

P

K

Ca

Cr

Mn

Fe

Ni

Cu

Zn

Ag

Ba

Pb

Average weight percent (ppm)

173

38.7

411

104

530

0.41

25.4

17.2

2.99

5.76

93.9

0.17

0.52

1.08

315

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A.D. Murphy-Leonard, et al.

RD

LD

RD

Fig. 1. Pole figures showing the initial texture with the basal poles aligned perpendicular to the loading direction. RD: Radial Direction; LD. Loading Direction. Fig. 2. Schematic of the diffraction experiment detailing the specimen geometry (specimen coordinate system: [X, Y, Z] in relation to the detector as well as the coordinate systems. The detector coordinate system can either be described using the rectangular coordinate system [X′, Y′] or a polar coordinate system [2θ, η′], where 2θ is the Bragg angle, η′ is the azimuthal angle, and D is the distance from the sample to the detector. During the experiment, the laboratory system is fixed while the sample is free to rotate about the loading axis defined by angle, ω [42]. An example of the continuous diffraction rings and the HEDM integration areas (Red boxes) are also shown. ND: Normal Direction, LD: Loading Direction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

D

Debye Scherer Rings

rate was reduced such that an entire cycle was completed in 480 s. Throughout the cycle, 240 images were collected with exposure times of 2 s. Each image number corresponds to a diffraction measurement.

Table 2 Maximum cyclic compressive and tensile stress at Cycle 2 for 0.40%, 0.52%, and 0.75% total strain amplitudes.

3. Results In this section, the experimental results provided by in-situ HEXD techniques are reported. The loading axes of all fatigue specimens were parallel to the extrusion direction. Thus, the c-axis of the majority of grains was normal to the loading direction and it was possible to activate {1 0 1¯ 2} 〈1 0 1 ́ 1〉 extension twinning during compression in these grains. Twinning was characterized using HEXD which allowed quantification of the relationship between twinning-detwinning and the intensity evolution of the basal {0 0 0 2} peak during cyclic loading. The data upon which this paper is based can be found at the Materials Commons at https://doi.org/doi:10.13011/m3-cfgh-vh23.

Total Strain Amplitude (%)

Maximum Tensile Stress (MPa)

Maximum Compressive Stress (MPa)

0.40 0.52 0.75

50 65 ± 0.7 68 ± 2

−47 −51 ± 3 −52 ± 0.0

for Cycle 2. This is a well-known and frequently observed phenomena and is related to the differences in deformation mode between tension and compression loading. In tension the dominant deformation mode is dislocation motion while in compression, although dislocations are no doubt present, the dominant deformation mode is extension twinning [12,14]. This results in higher peak stresses in tension (due to hardening from dislocation entanglement) compared with compressive loading. The tension-compression asymmetry found at the higher strain amplitudes was not observed in samples strained at 0.4% total strain amplitude. This is related to the absence of extension twinning in compression at the lower strains where deformation is assumed to be entirely due to dislocation slip. Similar results were reported by Yu et al, in pure Mg [3]. Fig. 3 shows the evolution of the maximum cyclic stress in compression and tension for each strain amplitude as a function of cycles. For the three strain amplitudes, the maximum tensile stresses at the

3.1. Macroscopic stress-strain response The macroscopic stress-strain history was monitored through-out the in-situ HEXD experiment, providing stress-strain hysteresis loops and a record of the peak tension and compression stresses as a function of fatigue cycles. These measurements were conducted at three different total strain amplitudes: 0.75%, 0.52%, and 0.4%. As expected, there was a significant tension-compression strength asymmetry at 0.52% and 0.75% total strain amplitudes. Table 2 shows these values 316

b). A

50 30 10

-10 0

0.4 0.8 Strain (%)

-30

Basal {0002} Peak Intensity Normal Direction

-70

e). d).

-0.8

-0.4

50 30 10 -10 0 -30

B

C-2

T-2 0.4 0.8 Strain (%)

f).

-50 -70

h).

-0.4

Stress (MPa)

Cycle 200

3.2. In-situ HEXD measurements

50 30 10

-10 0

-50 B

A

70

-30

Figs. 4, 5 and 6 shows the hysteresis loops for total strain amplitudes of 0.75%, 0.52%, and 0.4%, respectively and the evolution of the in-situ HEXD basal {0 0 0 2} peak intensity. It should be noted that after each HEXD measurement cycle (at zero strain), the test was paused to collect a pole figure resulting in some minor stress relaxation that is present in Figs. 4 and 5. The evolution of the X-ray peak intensity from scattering in both the loading direction and the direction normal to the loading direction, i.e., normal to the extrusion direction, was tracked as a function of cycles for each strain amplitude. In each HEXD intensity figure, the different stages of loading are indicated, i.e., tensile loading until the maximum tensile strain is reached at A, after which tensile unloading occurs until zero strain is reached; this is followed by compressive loading until the compressive maximum strain is reached at B and ending with compressive unloading back to a strain of zero. For each cycle, the maximum tensile strain is indicated by the letter A and the maximum compressive strain is denoted by B. The stars on each figure (e.g., C1 in Fig. 4a) represent points of interest and will be discussed throughout the results section. We note that ‘kinks’ in the macroscopic stress-strain response at 0 strain in cycles 2, 200, and 500 are due to small amounts of relaxation that occurred during separate, unreported pole figure measurements. The initial intensity of the basal {0 0 0 2} peak in the loading direction was zero. As stated in the previous section, a majority of the parent grains had their c-axis oriented normal to the loading direction, therefore when the parent grains underwent extension twinning, their c-axis was reoriented 86.3° towards the loading direction. This reorientation can be related to changes in the {0 0 0 2} peak intensities in

0.4 Strain (%)

0.8

i).

-70

k).

-0.4

Stress (MPa)

Cycle 500

70

A

50 30 10

-10 0 -30

B

4000 3000 2000 1000

C-1

A

0 0

40

0

40

B

80 120 160 Image Number

200

240

A

65000

Tensile Loading

8000 7000 6000 5000 4000 3000 2000 1000 0

T-2 0

B

80 120 160 Image Number

Tensile Unloading

73000

240

Compressive Unloading

Compressive Loading

C-2

A 40

200

B

80 120 160 Image Number

200

240

70000

67000 B

A

64000 0

40

Tensile Loading

12000

80 120 160 Image Number

Tensile Unloading

200

240

Compressive Unloading

Compressive Loading

8000 6000 4000

C-200

2000

B

A

0 0

40

68000

80 120 160 Image Number

200

240

200

240

66000

64000 A

62000 0

40

Tensile Loading

12000

B 80 120 160 Image Number

Tensile Unloading

Compressive Loading

Compressive Unloading

10000

j).

-0.8

5000

10000

g).

-0.8

Compressive Unloading

67000

Basal {0002} Peak Intensity Normal Direction

half-life were 63 MPa, 62 MPa, and 50 MPa, respectively. The maximum compressive stresses were approximately the same for all levels of applied cyclic strain and at the half-life were −52 MPa, −53 MPa and −47 MPa, respectively. At both 0.75% and 0.52% total strain amplitude, a tension-compression strength asymmetry was found, and the stresses reached in tension were higher than those reached in compression. The asymmetry was reduced at the lower strain amplitude of 0.4%. At strain amplitudes of 0.52% and 0.75%, slight hardening was observed during the first ten cycles followed by a hardening plateau until cycle 400 or 500, respectively, after which softening occurred until failure. This strain hardening plateau has also been observed in other alloys that deform by twinning including HCP Mg alloys [9,16], Zr alloys [35], and the shape memory alloy, NiTi [36]. At the strain amplitude of 0.4%, the stress-strain loops were cyclically stable and no significant variation in the maximum tensile and compressive stresses was observed for cycles up until 3000 at which point softening occurred until failure.

A

70

Stress (MPa)

Cycle 2

Compressive Loading

69000

Basal {0002} Peak Intensity Loading Direction

Fig. 3. The maximum stress in tension and compression as a function of fatigue cycles at the total strain amplitudes of 0.4%, 0.52%, and 0.75%.

Tensile Unloading

6000

71000

Basal {0002} Peak Intensity Loading Direction

C-1

Tensile Loading

7000

73000

c).

-50

B

Basal {0002} Peak Intensity Normal Direction

-0.4

-50 -70

0.4 0.8 Strain (%)

l).

Basal {0002} Peak Intensity Normal Direction

-0.8

70

Basal {0002} Peak Intensity Loading Direction

Cycle 1

Stress (MPa)

a).

Basal {0002} Peak Intensity Loading Direction

International Journal of Fatigue 125 (2019) 314–323

A.D. Murphy-Leonard, et al.

8000 6000 C-500

4000 2000

B

A

0 0

40

66000

80 120 160 Image Number

200

240

200

240

64000

62000 A

60000 0

40

B 80 120 160 Image Number

Fig. 4. Cyclic stress-strain loops and corresponding X-ray peak intensity of the basal {0 0 0 2} peak for tests conducted at a total strain amplitude of 0.75% (a–c) Cycle 1, (d–f) Cycle 2, (g–i) Cycle 200, & (j–l) Cycle 500. HEXD peak intensities in the Loading Direction (b, e, h, k) indicate the onset of twinning and detwinning; HEXD peak intensities in the Normal Direction (b, c, f, i, l) indicate the activation of other slip systems. Note: Vertical lines at Image 0 and Image 120 are at zero strain. Vertical lines at Image 60 and 180 are at peak tensile strain and peak compressive strain, respectively. 317

International Journal of Fatigue 125 (2019) 314–323

a). Cycle 1

Stress (MPa)

b). A

60 40 20 0

-0.6

-0.4

-0.2

-20

0

0.2

0.4

0.6

Strain (%)

Basal {0002} Peak Intesnity Loading Direction

A.D. Murphy-Leonard, et al. Compressive Unloading

the loading and normal directions and is directly related to the degree of twinning and detwinning that occurs during loading. The initial high peak intensity in the normal direction was related to the volume fraction of parent grains with their c-axis perpendicular to the loading direction. These grains were favorably oriented for extension twinning during compression. The peak intensity data in Figs. 4–6 was plotted as a function of image number (e.g., in Fig. 4b, c, e and f). The image number corresponds to the diffraction measurement and 240 diffraction measurements were taken throughout each cycle. An increase in the intensity in the loading direction indicated an increase in twinning while a decrease was related to the degree of detwinning, that is, the removal and/or narrowing of those twinned regions. Concurrently a decrease or increase in intensity in the normal direction was indicative of the volume fraction of regions that have reoriented their c-axis due to twinning or detwinning. Thus, the maximum in the intensity for the {0 0 0 2} X-ray peak in the loading direction (as shown in Fig. 4b) corresponds to a minimum in the intensity for the {0 0 0 2} X-ray peak in the normal direction (as shown in Fig. 4c). At 0.75% total strain amplitude (Fig. 4a–c), during Cycle 1 the intensity of the basal {0 0 0 2} peak in the loading direction remained zero until the applied stress reached a value of −52 MPa (indicated by C-1) at which point the X-ray peak intensity began to increase until it reached the maximum compressive strain (indicated by B). Upon reversal to compressive unloading the X-ray peak intensity immediately began to decrease until the end of cycle 1. This increase in intensity in the loading direction during compressive loading is tied to the onset of twinning, that is, the regions of the parent grains that are reorienting by 86.3° and the decrease in intensity during the load reversal is caused by detwinning. This detwinning process is also reflected by the intensity changes in the normal direction (Fig. 4c) where, during compressive loading, the intensity began decreasing at C-1 and continued to decrease until the maximum compressive strain was reached. At this point, the X-ray peak intensity began to increase until the end of the first cycle. At the end of cycle 1, the intensity did not return to zero or the background intensity indicating that all of the twins were not detwinned during compressive unloading. During the initial tensile loading of the following cycle (Cycle 2) the intensity in the loading direction immediately returned to zero (indicated by T-2), marking the exhaustion of detwinning at a stress of 20 MPa. This stress at the end of detwinning was referred to as the detwinning exhaustion stress. After that the intensity remained zero until the applied stress reached a value of −44 MPa (C-2). At C-2 the intensity began increasing and continued until it reached the maximum compressive strain indicating that twinning began at the compressive stress, C-2, in the second cycle. As the compressive unloading of Cycle 2 begins, the X-ray peak intensity immediately began decreasing showing that detwinning was occurring until the end the cycle. By Cycle 200 (Fig. 4g–i), the detwinning behavior changed, where the twins formed during compression were not completely detwinned and detwinning occurred until the maximum tensile strain was reached indicated by the decrease in intensity in the loading direction to its minimum at Point A. The X-ray peak intensity in the loading direction did not return to zero indicating that a finite volume fraction of residual twins remained in the material throughout the cycle. During compressive loading, the intensity increased indicating the onset of cyclic twinning. The behavior during Cycle 500 is similar to that of Cycle 200, where the intensity did not return to zero during tensile loading, but detwinning did occur until the maximum tensile strain was reached. The intensity at the maximum tensile strain of Cycle 500 was higher than that of Cycle 200 indicating that the volume fraction of residual twins increased with increasing cycles. To quantify the volume fraction of twins formed as a function of cycles, the apparent twin volume fraction, ϕ, was characterized using the relationship:

6000 4000 2000 C-1

A

0 0

50

100

B

150

200

250

200

250

Image Number Basal {0002} Peak Intensity Normal Direction

c).

-60

C-1

Compressive Loading

8000

-40 B

Tensile Unloading

Tensile Loading

10000

79000 78000 77000 76000 75000 74000 73000 72000 0

50

100

150

Cycle 2

Stress (MPa)

e). d).

A

60 40 20

T-2

0 -0.6

-0.4

-0.2

-20

0

0.2 0.4 Strain (%)

0.6

Basal {0002} Peak Intesnity Loading Direction

Image Number 10000

f).

-60

Compressive Unloading

6000 4000 2000 T-2 0

C-2

A

0 50

100

B

150

200

250

200

250

Image Number Basal {0002} Peak Intensity Normal Direction

C-2

Compressive Loading

8000

-40 B

Tensile Unloading

Tensile Loading

79000 78000 77000 76000 75000 74000 73000 72000 0

50

100

150

h). Cycle 200

Stress (MPa)

g).

A 60 40 20 1

0 -0.6

-0.4

-0.2

-20

0

0.2

0.4

0.6

Strain (%)

Basal {0002} Peak Intesnity Loading Direction

Image Number Compressive Unloading

6000 4000 2000 B

A

0 0

50

100

150

200

250

200

250

Image Number Basal {0002} Peak Intensity Normal Direction

i).

-60

Compressive Loading

8000

-40 B

Tensile Unloading

Tensile Loading

10000

75500 75000 74500 74000 73500 73000 72500 72000 0

50

100

150

j). Cycle 500

Stress (MPa)

k). A

60 40 20 0

-0.6

-0.4

-0.2

-20

0

0.2 0.4 Strain (%)

0.6

Basal {0002} Peak Intesnity Loading Direction

Image Number

l).

Compressive Loading

Compressive Unloading

6000 4000 2000 A

0 0

50

B 100

150

200

250

200

250

Image Number Basal {0002} Peak Intensity Normal Direction

-60

Tensile Unloading

8000

-40 B

Tensile Loading

10000

72000 71500 71000 70500 70000 69500 69000 0

50

100

150

Image Number

Fig. 5. Cyclic stress-strain loops and corresponding X-ray peak intensity of the basal {0 0 0 2} peak for tests conducted at a total strain amplitude of 0.52% (a–c) Cycle 1, (d–f) Cycle 2, (g–i) Cycle 200, & (j–l) Cycle 500 HEXD peak intensities in the Loading Direction (b, e, h, k) indicate the onset of twinning and detwinning; HEXD peak intensities in the Normal Direction (c, f, i, l) indicate the activation of other slip systems. Note: Vertical lines at Image 0 and Image 120 are at zero strain. Vertical lines at Image 60 and 180 are at peak tensile strain and peak compressive strain, respectively. 318

International Journal of Fatigue 125 (2019) 314–323

A.D. Murphy-Leonard, et al.

Stress (MPa) -0.5

-0.3

Cycle 2 Cycle 2000

25 5

-0.1 -15

0.1

0.3

0.5

Strain (%)

-35 B

b).

A

Cycle 200

45

Basal {0002} Peak Intensity Normal Direction (A.U.)

a).

Tensile Loading

58000 57500 57000 56500 56000 55500 55000 54500 54000 53500 53000

Compressive Loading

Compressive Unloading

Cycle 2000

Cycle 200

Cycle 2

0

-55

Tensile Unloading

40

80

120 160 Image Number

200

240

Fig. 6. Cyclic stress-strain loops and corresponding X-ray peak intensity of the basal {0 0 0 2} peak for tests conducted at a total strain amplitude of 0.4%. (a) Stressstrain loops for Cycles 2, 200, & cycle 2000; (b) HEXD of the X-ray peak intensity for the basal {0 0 0 2} planes in the normal direction. Note: HEXD measurements in the loading directions indicated intensities of zero, indicating no twinning. Note: Vertical lines at Image 0 and Image 120 are at zero strain. Vertical lines at Image 60 and 180 are at peak tensile strain and peak compressive strain, respectively.

ϕ=

ILD 0 IND

two-three times (from 20 to 30 MPa to 55–60 MPa). Similar behavior was also observed in the sample cycled at 0.52% total strain amplitude (Fig. 5). Fig. 5 shows the hysteresis loops for cycles 1, 2, 200 and 500 (at the fatigue half-life). As compressive load was applied in Cycle 1, twinning began at a stress of −52 MPa (indicated by C-1). During tensile loading of the next cycle, the intensity returned to zero at 15 MPa (T-1) and remained zero until compressive loading commenced. The diffraction data suggests that the exhaustion of detwinning occurs at this point, indicated by the decreasing intensity of the basal {0 0 0 2} peak in the loading direction up until this point and the increasing intensity in the normal direction until the maximum tensile strain is reached. During cycle 2, twinning began at a stress of −46 MPa (C-2), indicated by the increase intensity from this point until the maximum compressive strain is reached. Similarly, to the specimen deformed to 0.75% strain, as tensile load is applied in Cycle 200, the Xray peak intensity in the loading direction decreased until the maximum tensile strain was reached, but never returned to zero due to the presence of residual twins. The stress at which extension twins were initiated also gradually increased with cycles as well as the stress at the completion of detwinning (Fig. 8a and b). The twin intensity and the twin volume fraction at 0.52% total strain amplitude significantly increased during the first five cycles (Fig. 7a and b). At 0.4% total strain amplitude, during cyclic loading up to 2000 cycles, no diffracted intensities in the loading direction were detected. Thus, only the intensity of the {0 0 0 2} basal peak in the normal direction was reported in Fig. 6. The diffraction data suggests that the plastic deformation does not appear to be facilitated by the same extension twinning mechanism observed in the 0.75% and 0.52% strain amplitude experiments, since no increase in intensity in the {0 0 0 2} basal peak along the loading direction was observed.

(2)

0 where IND is the initial basal {0 0 0 2} X-ray peak intensity of the parent grains in the normal direction and ILD is the basal {0 0 0 2} X-ray peak intensity in the loading direction at the maximum compressive strain. The value ILD is termed the twin X-ray peak intensity and taken to be a measure of the maximum twin volume fraction during the cycle. It should be noted that this apparent twin volume fraction is measured for the entire volume of the sample illuminated by the high energy X-ray beam which is estimated to be 7.8 mm2. The azimuthal data was averaged over an azimuthal length of 5 degrees. The twin X-ray peak intensity and the twin volume fraction are plotted as a function of number of fatigue cycles in Fig. 7. The twin volume fraction more than doubled in the first five cycles and then gradually increased indicating that the most significant twinning occurs very early during cyclic loading. For the first 100 cycles, near-complete twinning and detwinning occurs, where the majority of the twins formed under compression are detwinned under the tensile loading of the following cycle. The stress at the initiation of twinning during the first 100 cycles is plotted as a function of cycles in Fig. 8a. It was determined that the twin initiation stress gradually increased with cycles. For example, in the sample fatigued at a total strain amplitude of 0.75%, in the first compression cycle, twinning initiated at −52 MPa but this stress decreased to −44 MPa in Cycle 2, indicating that additional plastic deformation occurred in the second cycle, resulting in the earlier formation of twins as the second cycle progressed. For the detwinning process, the stress at the completion of detwinning during tensile loading was characterized and is shown in Fig. 8b. This stress also gradually increased throughout the first 100 cycles indicating that more twins are formed during the previous cycle and therefore a higher stress was required for completely detwinning during the tensile loading of the following cycle. Interestingly, over the next several hundred cycles of loading for these samples, the twinning stress decreased by roughly five times (from −50 MPa to −10 MPa) while the detwinning exhaustion stress increased by roughly

b). Twin Volume Fraction (%)

a). 14000 Twin Intensity

12000 10000 8000 6000 0.75% Total Strain Amplitude 0.75% Total Strain Amplitude, Sample 2 0.52% Total Strain Amplitude 0.52% Total Strain Amplitude, Sample 2

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20 18 16 14 12 10 8 6 4 2 0

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1

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Fig. 7. The (a) twin X-ray peak intensity (at the maximum compressive strain) and (b) apparent twin volume fraction (at the maximum compressive strain) calculated using Eq. (1) at both 0.75% and 0.52% total strain amplitudes. 319

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b).

0

-10 -20 -30 -40

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-50

Detwinning Exhaustion Stress (MPa)

Twin Initiation Stress (MPa)

a).

-60 1

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60 50 40 30 20

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10 0

1000

1

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100

1000

Fig. 8. (a) The stress at the initiation of twinning and (b) the stress at the completion of detwinning for both 0.75% and 0.52% total strain amplitudes.

strain) cycle was applied to the sample (Fig. 9d), the twins were not completely detwinned indicating that residual twins remained in the material after 104 cycles. There was also low indexing of Kikuchi patterns in the twinned regions in Fig. 9d indicating a build-up of dislocation structures as discussed in more detail in the discussion section.

3.3. Characterization of persistent and residual twinning using electron back scatter diffraction EBSD imaging was used to characterize the spatial nature of cyclic twinning and detwinning behavior on the sample surface during cyclic loading. Strain-controlled, ex-situ interrupted cyclic tension and compression experiments were performed at 0.6% total strain amplitude on rectangular flat specimens. The specimen surface was polished prior to loading and characterized after each loading step using EBSD. The results are shown in Fig. 9 (note: a minor number of twins were observed in the as-polished sample which were induced during mechanical polishing). In Fig. 9a, twins formed in regions outlined by black circles after initial compression to −0.6% strain (cycle 1). After tensile loading to +0.6% strain those same twins detwinned and disappeared. After a second compressive strain of −0.6% was applied to the sample, twins formed in those same grains and in the same locations as Cycle 1, indicative of what we term “persistent twin formation”. This persistent twin formation and subsequent detwinning of persistent twins was recorded every 25 cycles for approximately 100 cycles. Cyclic loading continued for an additional 103 cycles and twinning continued to reoccur in the same locations as cycles 1 and 2. As shown in Fig. 9c, with the exception of this “persistent twin formation”, no new twin activity was observed in this region. During cycle 104, after an additional quarter tension (+0.6%

a).

b).

c) .

d).

4. Discussion Using HEXD, the influence of cyclic deformation on extension twinning behavior has been characterized in unalloyed magnesium. The normalized X-ray peak intensity for extension twins was used to quantify the apparent twin volume fraction at the maximum compressive stress (Fig. 7b) which increased with application of fatigue cycles. This increase in apparent twin volume fraction was particularly pronounced early in the fatigue life. The apparent twin volume fraction more than doubles in the first five cycles at strain amplitudes of 0.52% and 0.75%. After this initial rapid increase, the twin volume fraction gradually increases until it reached a plateau. This is similar to results of Wu et al, who used neutron diffraction to characterize extension twinning in the wrought magnesium alloy ZK 60 [12]. The increase in twin volume fraction indicates that twinning becomes easier as fatigue cycling continues. By coupling the information from the in-situ HEXD technique and the cyclic stress-strain history, the compressive stress at which twinning Fig. 9. Electron back scatter diffraction patterns showing residual twins in fine-grained pure Mg (45 μm): (a) twins form in grains after compression to −0.6% strain (black circles denote areas of interest), (b) those same twins are removed after tension to +0.6% strain in areas outlined in black circles strain, (c) the same twins return to the same grains after 104 cycles are applied to the sample, and (d). when a quarter tension (+0.6% strain) cycle is applied after 104 cycles the twins are not completely removed confirming that residual twins remain in the material. All EBSD measurements were in the unloaded condition.

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initiates was quantified. At strain amplitudes of 0.52% or greater, the stress at which twins are initiated is substantially reduced as cycling continues (Fig. 8a). This is consistent with the above observation that twinning appears to be easier as cycles are increased. It is generally understood that twins initiate at grain boundaries and, in particular, at grain boundaries with features and stress states that promote twin nucleation [23,37]. For the initial compression cycle, Beyerlein and Tome' have proposed a probabilistic model that considers twin nucleation as a statistical process and that twins nucleate and grow when a specific stress state and grain boundary dislocation configuration are present [37]. As cycling progresses the defects in these regions might be expected to increase, which appear to lead to easier twin formation thus leading to the reduction in the initiation stress and increase in volume fraction observed in the current investigation and the observation of “persistent twins” which will be discussed later. Upon reversal of the compressive load cycle, this study and others [12,19,38] have observed a narrowing of twins, a process known as detwinning. Detwinning begins immediately upon load reversal and the amount of detwinning increases as load is decreased to zero load in the cycle. On the tensile portion of the next cycle, the amount of twins continues to decrease until this detwinning is completed and all twins are removed from the structure. It should be noted that the stress at which complete detwinning occurs will be referred to as the detwinning exhaustion stress throughout this discussion. In this study, we have used the coupled results from the in-situ HEXD technique and the cyclic stress-strain history to quantify the detwinning exhaustion stress. The detwinning exhaustion stress gradually increased with cycling (Fig. 8b). This increase appeared to correspond with the increase in the twin volume fraction measured at the peak compressive stress. During early cycles, as the twin volume fraction more than doubles, the detwinning exhaustion stress also doubles. We suggest that when a larger volume fraction of twins is available to be detwinned, a consequently higher tensile stress is needed for complete detwinning to occur. This is consistent with the observations of at least two other investigations on Mg alloys [12,38]. In Mg alloys, twins created during previous compressive loading gradually disappear during compressive unloading and/or tensile reloading. This detwinning has a significant effect on the stress-strain response of the material since it requires reorientation of portions of the grain back to the original orientation (prior to twinning) via a change in the size of the twin or complete removal of twin boundaries [39,40]. As mentioned, in the current study at both strain amplitudes, the detwinning began immediately upon reversal of the maximum compressive strain. This was evident as the twin intensity continually decreases from the compressive peak until the end of the cycle. This has significant ramifications for how this detwinning process should be included in crystal plasticity models of cyclic deformation, since it indicates that reversed plastic deformation occurs almost immediately upon unloading. For the first 100 cycles at 0.75% strain amplitude and 200 cycles at 0.52% strain amplitude complete twinning-detwinning occurs in which the twins that formed during compressive loading appear to be fully detwinned during reverse loading in tension. Despite the fact that complete detwinning occurs, the apparent twin volume fraction measured at the maximum compressive stress generally increases. After several hundred fatigue cycles, a point is reached at which complete detwinning no longer occurs and residual twins appear to be retained throughout the entire cycle. Once this condition is reached the residual twins appear to increase linearly with cycles as shown in Fig. 10. EBSD analysis (e.g. Fig. 9d) also confirmed that residual twins remain in the material after a number of cycles. Within these residual twin regions, the EBSD Kikuchi patterns are poorly indexed which is an indication of dislocation accumulation within the twin due to successive cycling. This suggests that at a certain point in cycling, the accumulation of dislocations in the twin regions inhibits complete detwinning and “locks” in the residual twin structure. Similar behavior has been

7000

0.75% Total Strain Amplitude 0.75% Total Strain Amplitude, Sample 2 0.52% Total Strain Amplitude 0.52% Total Strain Amplitude, Sample 2

6000 5000 4000 3000 2000 1000 0 1

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Cycles

Fig. 10. The twin intensity (intensity of the [0 0 0 2] basal peak) at the maximum tensile strain for both 0.75% and 0.52% total strain amplitudes.

observed in several other studies [7,12,19,26]. A diffraction study by Brown et al showed that the residual twin content increased with cycling in the Mg AZ31B alloy [19]. Mirza et al found residual twins in regions near the fracture surface after low cycle fatigue in the Mg alloys, GW103K and AM30 [7]. In a neutron diffraction study by Wu et al. of Mg AZ31, residual twins were observed after only 20 cycles were applied at a large cyclic strain of 2% [26]. The residual twin content contributes to the hardening of the material as twin boundaries can act as barriers to dislocation motion. It has been proposed that residual twins may also “retwin” in situations in which there is repeated growth of the residual twin as cycling continues [24]. This retwinning is the repeated cyclic growth of a residual twin that has not been completely detwinned [41]. In the current investigation, persistent twin formation was observed during LCF using EBSD analysis. During persistent twin formation, twin activity reoccurs in the same locations as cycling proceeds. Although the location of the initial twin nucleation process may be random in nature [37], subsequent persistent twins occur in precisely the same location due to the unique characteristics of the twinning site. In the observed areas, after a 100 cycles no new twin activity is shown in the material which may explain the plateau in the twin volume fraction that was observed. These persistent twins may be similar to persistent slip band (PSB) formation during cyclic loading [42]. A PSB is defined as a zone in which low energy dislocation structures are stabilized and localized during cyclic deformation [42]. Beyerlein et al. [37] and Wang et al. [23] have suggests that twins nucleate at grain boundaries where partial dislocations and multiple twinning dislocations exists and in cases where these nucleation sources don’t exist reactions are needed to produce them. High stress concentrations present at grain boundaries can provide the energy needed to overcome energetic barriers to activate these reactions [23]. When the defects needed for nucleation exist at the grain boundary, twin initiation from that site is favored. In this study, the observation that twins continue to occur at the same location during cyclic deformation appears to support this mechanism. It is well understood that PSB’s are favorable sites for crack initiation. Although this was not the subject of the current work, we may anticipate that persistent twins may play a similar role. Yu et al found that during cyclic loading of pure Mg twin tips were the sites of dominant crack initiation and related this behavior to a stress concentration in these initiation zones [3]. Future studies are warranted to elucidate the role of alloying on persistent twin formation and fatigue crack initiation. This investigation was part of a larger effort within the Center for PRedictive Integrated Structural Materials Science (PRISMS Center) which is developing a broad capability to accelerate scientific discovery and design of new alloys [31,43]. The goal of the current study was to establish a baseline reference for cyclic twinning and detwinning phenomena for unalloyed magnesium. This is being used to identify critical phenomena (e.g. evolution of twin volume fraction, detwinning and changes in twinning and detwinning exhaustion stresses during cycling) which must be included in models such as the PRISMS-Plasticity crystal 321

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plasticity finite element model [31] to provide useful predictions of cyclic stress-strain response of magnesium and magnesium alloys. The insights provided by the current investigation will also serve as a reference for future experimental and modeling research on alloying effects on cyclic twinning and detwinning, cyclic stress-strain response and LCF behavior.

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5. Conclusions The cyclic twinning-detwinning behavior of unalloyed Mg was studied using in-situ high energy X-ray diffraction techniques and related to the cyclic stress-strain response. The major conclusions are as follows: 1. An increase or decrease in the {0 0 0 2} basal X-ray peak intensity in the loading direction was observed during cyclic loading and can be directly related to {1 0 1¯ 2} 〈1 0 1 ́ 1〉 extension twinning and detwinning. 2. The twin volume fraction and twin intensity doubles in the first five cycles, then gradually increases until failure. This finding indicates that twin evolution is more active during the early stages of fatigue loading. 3. The compressive stress at which twinning initiates decreases with cycling, indicating that twin-associated plastic flow is increasing on every cycle with twins forming earlier in the cycle. 4. Detwinning begins immediately upon load reversal. Near-complete detwinning occurred for the first few hundred cycles indicating that all twins formed during the compressive load cycle detwinned during reversed loading. 5. During a cycle, the stress at which detwinning is completed, known as the detwinning exhaustion stress, increases with repeated cycling; as the twin volume fraction increases, a higher tensile stress is needed to detwin the material during the following cycle. At higher numbers of cycles, complete detwinning was not observed and HEXD results indicated that residual twins remain in the material throughout each cycle and the amount of these residual twins increased with increasing cycles. 6. The above conclusions were for strain amplitudes of 0.52% and above. At an applied strain of 0.4% no indication of extension twinning was observed in either the stress-strain loop behavior or in the HEXD measurements. Acknowledgments This work is supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Science and Engineering under Award #DE-SC0008637 as part of the Center for PRedictive Integrated Structural Materials Science (PRISMS) at the University of Michigan. ADM also acknowledges the support of the National Science Foundation Fellowship. This work is based upon research conducted at the Cornell High Energy Synchrotron Source (CHESS) which is supported by the National Science Foundation under award DMR-1332208. We thank Bruce Williams and CanmetMATERIALS for providing the materials for this research. We also thank Dr. Tracy Berman and Dr. Qianying Shi who assisted in the HEXD measurements. The data on which this paper was based is available on Materials Commons at https://doi.org/doi:10.13011/m3-cfgh-vh23. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijfatigue.2019.04.011. References [1] Bettles C, Gibson M. Current wrought magnesium alloys: strengths and weaknesses.

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