Surface Relief Formation of Cyclic-Loaded Coarse-Grained Aluminum Polycrystals with Point Defect Clusters

Abstract

Surface relief formation processes of the high cyclic-loaded coarse-grained aluminum polycrystals with point defect clusters were investigated. Until the loading of 1 × 10⁵ cycles with the stress ratio of −1 and the maximum stress of 8.0 MPa, the coarse ribbon-like primary persistent slip markings (PSMs) consisting of extrusions and intrusions had been formed, and the average extrusion height of the PSMs had reached 2.0 µm. This value was much higher than that of the ordinary aluminum single crystal. The high mobile dislocation density accompanied by the dislocation channeling effect inside the persistent slip bands (PSBs) were considered to produce the high extrusions. Until the loadings to 2.4 × 10⁵ cycles with the stress ratio of −1 and the maximum stress of 8.0 MPa, activities of the primary PSBs had been weakened or terminated, and instead, the secondary slips had been activated and deformed the shapes of the preexisting primary PSMs. And the deep brittle-like cracks along the grain boundaries (GBs) were observed. The accumulation of the dislocations and the vacancies into the GBs were considered to be the trigger for the energy reduction of the GBs as the interfaces and the brittle-like cracks formation.

Fig. 16 (a) SEM image showing the deep brittle-like crack observed after the loading of 2.4 × 10⁵ cycles with the maximum stress of 8.0 MPa at the GB between “Grain C” and “Grain D”. (b) Enlarged image of the crack. A huge number of faint PSMs were intersecting with the GB where the crack opened.

1. Introduction

Since the historical report of Forsyth¹⁾ showing the “extrusions” of the cyclic loaded aluminum-copper alloy was published in the year of 1953, a number of researches regarding the fatigue processes of the face-centered-cubic metals have been carried out.^2–29) The term “persistent slip band (PSBs)” was used by Thompson et al. in their literature of the fatigue fracture of Cu.²⁾ As widely recognized, major catastrophic failures of the actual structural materials in services are caused by the fatigue triggered by the formation of PSBs. Since Laufer et al.^3,4) indicated the dislocation structures of the PSBs, the microstructures of the PSBs have been characterized by the dense walls (PSB walls) of dislocations in a multipole arrangement perpendicular to the Burgers vector of the primary slip system, i.e., edge dislocation multipoles, separated by the almost-dislocation-free zone parallel with the walls. Under the loadings, the free primary edge dislocations are bowing out of the walls and the primary screw dislocations are linking the walls. By utilizing the Discrete Dislocation Dynamics (DDD),^30–32) Erel et al.³³⁾ indicated the simulation results of dislocation structures inside the PSBs. Based on the motions of the screw dislocations, they developed several patterns of the prismatic dislocation loop formations under cyclic loading.

The reliefs appear where PSBs are meeting surfaces, i.e., persistent slip markings (PSMs), are usually accompanying the extrusions and intrusions. Man et al.²⁰⁾ categorized the mature extrusions of the PSMs observed on face-centered-cubic metals as “tongue-like extrusion”, “ribbon-like extrusion” and “protrusion with superimposed extrusions and intrusions”. They mentioned that the “tongue-like extrusion” and “ribbon-like extrusion” can be observed in polycrystals and “protrusion with superimposed extrusions and intrusions” in single crystals. According to Essmann et al.,⁹⁾ Polák,^12,24) and Liu et al.,²⁹⁾ the extrusions are considered to be the result of volume expansions due to the generations and migrations of a large number of vacancies. These models are called the vacancy model.²⁰⁾ Production of vacancies in cyclic loaded metals has been proved by the electrical resistivity measurements by Polák.¹²⁾ Basinski et al.¹³⁾ examined the PSBs appeared on the surfaces of Cu single crystals by using their sharp corner technique, enabling detailed examinations. They classified the PSBs of Cu single crystals as Type I, Type II and Type III in terms of the testing temperature ranges, i.e., Type I: below 15 K, Type II: from 15 K to 250 K, and Type III: above room temperature. Type I extrusions are bulged and triangular shape, often bearing smooth extrusions and showing no evidence of intrusions. Type II extrusions meet the original surfaces at sharp angles and accompany the intrusions. Type III extrusions are long and wavy, accompanying the prominent intrusions and the isolated intrusions are also common. Basinski et al.¹³⁾ concluded that the vacancy models, at least low temperatures, cannot explain the PSB morphology.

Understanding the crack formation process is the most important and difficult task for the study of the fatigue phenomena. Basinski et al.¹³⁾ concluded that when the isolated intrusions (above mentioned Type III profiles) form, they become preferred crack sites, and when the large triangular protrusions (above mentioned Type II profiles) form, cracks invariably develop at the sharp notch. Zhang et al.²¹⁾ investigated the low-cycle fatigue cracking mechanisms of various face-centered-cubic metals such as Cu single crystals. They classified the fatigue cracking into the shear crack and the impingement crack. The shear crack occurs along the slip bands such as PSBs and deformation bands (DBs) caused by shear strain localization during the fatigue process. The impingement crack is originated at interfaces such as grain boundaries (GBs) by pileups of dislocations against the interfaces. Liu et al.²⁹⁾ developed a microstructure-based intergranular fatigue crack model of the face-centered-cubic polycrystals. They classified the PSB-GB interaction into the three categories, i.e., the dislocation transmission, the dislocation source activation, and the crack nucleation. They concluded that the GB fatigue cracks preferentially nucleate at high angle grain boundaries (HAGB) with poor plastic compatibility. According to them, the poor plastic compatibility of the GB is introduced by the transportations of the residual dislocations and the vacancies from the interior of the grain to the GB. Taking those conditions as factors of the GB decohesion energy increase, they estimated the critical shear stress for the crack nucleation at the GB.

As Basinski et al.¹³⁾ raised their questions regarding the vacancy model, we consider that the current vacancy models have not placed the importance on the roles of the dislocation glides themselves for the PSM formations. In the present study, surface relief formation of the cyclic loaded high-purity aluminum polycrystals with point defect clusters were investigated. The aluminum polycrystals used for the present study were prepared from 99.999% high-purity raw materials and rapid cooled from elevated temperatures to sub-zero refrigerants. As Tokuno et al.^34–40) revealed, plastic deformations of the face-centered-cubic metals with rapid-cooled-in point defect clusters such as dislocation loops proceed with the formation of the dislocation channels, i.e., “dislocation channeling”. Dislocation channels are highway-like-free areas where the point defect clusters are swept out through the interactions with the glide dislocations. Therefore, once the cleared, i.e., point defect clusters free, channels are formed, multiplications and glides of the following dislocations are concentrated inside the channels. Figure 1 shows transmission electron micrographs (TEM) of the cleared dislocation channels formed in rapid-cooled and uniaxially tensile-deformed aluminum single crystals.^34,35) According to Tokuno,³⁵⁾ the average microscopic shear strain inside the channel was estimated to be about 100% which was much higher than the macroscopic shear strain of the specimen. Mechanisms of the sweeping process of the several point defect clusters by glide dislocations were discussed by several authors.^41–44) Because the PSB formations are obviously dislocation-related matter, dislocation multiplications and glides inside the PSBs should be accelerated by a similar manner with the dislocation channeling. Therefore, the surface reliefs produced as the appearances of the PSBs, i.e., PSMs, may have strong correlations with the dislocation channeling. Zhang et al.²¹⁾ also expressed that slip bands may become a carrier and a channel to transport residual dislocations and vacancies from the interior of grains to GBs. Besides the expected channeling effects mentioned above, the coarse crystal grains grown by the heat treatment accompanying the elevated temperatures also led to deformation enhancement through the dislocation pileup effect. Obtained results through the present investigations were discussed by comparisons with several previous studies.

Fig. 1

TEM images of the dislocation channels of the primary slip systems in rapid-cooled aluminum single crystals tensile-deformed to macroscopic shear strains of (a) 0.3%, (b) 8.0% and (c) 16.0%.^34,35) These images were taken under the condition of $\boldsymbol{z} \cong [1\ \bar{2}\ 1]$ and g = 1 1 1. Dark spots are rapid-cooled-in point defect clusters (Frank-type dislocation loops), “T” tangled dislocation structures and “L” layered dislocation structures.

2. Experimental Procedure

Specimens used for the present study were prepared from 99.999% high-purity raw materials. From the cold-rolled to 4 mm thick plate, the materials were machined to the shapes as shown in Fig. 2. For avoiding the buckling during the cyclic loading, the gauge-part length between both grips was limited to 30 mm. For the heat treatment control, thermocouple was inserted into the hole (ϕ1.8 × 15 mm) of the specimens. In order to produce the point-defect-clusters, the specimens were heated to 893 K and kept for 3.6 ks and vertically dropped to salt water of which temperature was 253 K. After the heat treatment, specimens were electro-polished with solutions of HClO₄:200 cm³ and (CH₃CO)₂O:400 cm³ for the surface observations. Sizes of the polycrystalline grains observed in the present study were ranging between 1.5∼3.3 mm.

Fig. 2

Schematic diagram of the plate-shaped polycrystalline specimen for the present investigation. Thickness of the specimen was 4 mm. For avoiding the buckling during the alternate loading, its gauge-part length between both grips was limited to 30 mm. For the heat treatment control, thermocouple was inserted into the hole (ϕ1.8 × 15 mm).

After the pre-test treatment, to check the yield-stress, one of the specimens was uniaxially tensile deformed by a tensile machine with a crosshead speed of 0.1 mm/min. Figure 3 shows a relationship between the uniaxial nominal tensile stress and the elongation of the specimen. The stress values were determined by dividing the measured loads with the minimum cross section of the specimen, i.e., 8 × 4 mm². And the elongation was defined as the crosshead displacement, i.e., ΔL. The obtained nominal yield stress was 13.5 MPa which was about 4∼5 MPa higher than those of single crystals with point defect clusters.^36–40)

Fig. 3

A uniaxial nominal tensile stress vs. elongation curve of a specimen used for the present investigation. Crosshead speed of the testing was 0.1 mm/min and the stress values were determined by dividing the measured loads with the minimum cross section of the specimen, i.e., 8 × 4 mm². The elongation of the specimen was defined as the crosshead displacement, i.e., ΔL. The estimated nominal yield stress was 13.5 MPa.

The push-and-pull cyclic loadings were performed in a servo-hydraulic machine in air and at room temperature. The loading cycle was a sinewave with 1 Hz and the stress-ratio, i.e., minimum stress/maximum stress, was controlled to be −1. The maximum stresses of the cyclic loading tests were lower than the yield stress, i.e., 13.5 MPa.

Focusing on the dislocation glides, we conducted the investigations on the detailed surface morphology and its changes during the loading and the crack initiation behaviors supposed to link to the final failures of the specimens.

3. PSMs Observed after the Loading of 1 × 10⁵ Cycles with the Maximum Stress of 8.0 MPa

Figure 4 shows an optical micrograph of the surface morphology of the polycrystalline specimen after the loading of 1 × 10⁵ cycles with the maximum stress of 8.0 MPa. SEM images of the PSMs inside the highlighted grain of Fig. 4 are shown in Figs. 5 and 6.

Fig. 4

Optical micrograph of the surface morphology of the polycrystalline specimen after the loading of 1 × 10⁵ cycles with the maximum stress of 8.0 MPa. “LD” means the cyclic loading direction. SEM images of the PSMs inside the highlighted grain are shown in Figs. 5 and 6.

Fig. 5

SEM images in the enclosed areas of the highlighted grain of Fig. 4. Well-grown coarse primary PSMs consisting of the ribbon-like extrusions and intrusions had been developed. “GB” means grain boundary.

Fig. 6

(a) Enlarged image of Fig. 5(c). (b) Enlarged image of the enclosed area of (a). Coarse PSMs of several micrometers wide consisting of the typical ribbon-like extrusions and intrusions had been developed. Besides the primary PSMs, some faint secondary slips crossing the primary PSMs were observed.

Figure 5 shows scanning electron microscope (SEM) images of the enclosed areas in the highlighted grain of Fig. 4. Well-grown coarse primary PSMs consisting of the ribbon-like extrusions and intrusions had been developed. Figure 6(a) shows an enlarged image of Fig. 5(c), and Fig. 6(b) shows a further enlarged image of the enclosed area of Fig. 6(a). Several micrometers wide well-grown coarse primary PSMs consisting of the typical ribbon-like extrusions and intrusions were observed. Besides the primary PSMs, some faint secondary slips crossing the primary PSMs were also observed.

Figure 7 shows bird views of atomic force microscope (AFM) profiles of the PFMs inside the enclosed areas of the highlighted grain of Fig. 4. Figure 8(a) shows the AFM profiles of Fig. 7(a). Horizontal and vertical directions are defined as x and y axis, respectively. Crystallographic orientation of the grain was determined by using electron back scatter patterning (EBSP) with fixing the loading direction as the longitudinal axis of the patterning, i.e., x axis. The right faces of all extrusions were identified to be almost parallel with (1 1 1) plane which was defined as the primary slip plane on which primary dislocations inside the PSBs glide. And by the EBSP analysis, angle ζ between y axis and the primary slip direction $[\bar{1}\ 0\ 1]$ was determined as 44.6°. The maximum stress of this cyclic loading (8.0 MPa) was converted by multiplying the Schmid factor (0.490) determined by the EBSP analysis to the resolved shear stress as 3.92 MPa. As shown in Fig. 8(b), height of the extrusions measured by AFM, h, can be projected on the primary slip plane (1 1 1) along the primary slip direction $[\bar{1}\ 0\ 1]$ by the following equation.

  

\begin{equation} h_{\textit{ext}} = h/{\cos \zeta} \end{equation} (1)

The obtained h_ext of all extrusions observed in Fig. 7 were ranging between 0.6∼3.3 µm and their average was 2.0 µm. And widths of the PSMs measured along x axis, w, were ranging between 1.2∼7.0 µm and their average was 3.0 µm. In Fig. 8(c), brief schematic posted on the right of the sectioned view of an extrusion shows the presumed dislocation structures inside the extrusion. This schematic shows the dislocation structures developed on (1 1 1) planes and the arrows show $[\bar{1}\ 0\ 1]$, i.e., the primary slip direction and $[1\ \bar{2}\ 1]$, i.e., elongation direction of the primary edge dislocations. Under the cyclic loadings, the primary screw dislocations linking the PSB walls consisting of edge dislocation multipoles elongating along $[1\ \bar{2}\ 1]$ direction are considered to glide back-and-forth through the almost-dislocation-free zone parallel with the walls and gradually make the extrusions. Besides the dislocation glides, the vacancies produced by dragging of jogs of the screw dislocations and/or climb motion of the edge dislocations may migrate inside the PSBs and contribute to the build of the extrusions as Essmann et al.,⁹⁾ Polák,^12,20,24) and Liu et al.²⁹⁾ mentioned.

Fig. 7

Bird views of AFM profiles of the PSMs inside the enclosed areas of the highlighted grain of Fig. 4.

Fig. 8

(a) AFM profiles of Fig. 7(a). Horizontal and vertical directions are defined as x and y axis, respectively. The right faces of all extrusions were almost parallel with (1 1 1) plane. (b) Brief schematics of a bird view of the ribbon-like extrusion’s profile. ζ Is the angle between y axis and the primary slip direction b_P. Measured extrusions’ height h were converted into h_ext $( = \boldsymbol{h}/{\cos \boldsymbol{\zeta}})$. Average of the obtained h_ext of Figs. 7(a)∼7(e) was 2.0 µm. (c) Brief schematic posted on the right of the sectioned view of an extrusion shows the presumed dislocation structures inside the extrusion. This schematic shows the dislocation structures developed on (1 1 1) planes and the arrows show $[\bar{1}\ 0\ 1]$, i.e., the primary slip direction and $[1\ \bar{2}\ 1]$, i.e., elongation direction of the primary edge dislocations.

Zhai et al.¹⁴⁾ investigated the surface relief of aluminum single crystals after the push-and-pull cyclic loading at room temperature by using the acoustic microscope. Their plate-shaped specimen was grown by the critical strain-annealing method. The normal direction of the front surface of the plate-shaped specimen was [1 0 2], the loading direction was $[2\ 5\ \bar{1}]$, and the primary slip system was $[0\ \bar{1}\ 1](1\ 1\ 1)$. The cyclic loading was performed with 20 Hz and the resolved shear stress amplitude was controlled to be 4 MPa. According to their results, the height of the extrusions on the front surface, h, was 0.8 µm after 5 × 10⁶ cycles. Based on the crystallographic orientations of their specimen, the measured height, h, can be converted by the eq. (1) to h_ext = 0.84 µm. This converted value was much lower than the average, h_ext = 2.0 µm, of the present result. A period of the loading cycle of the present study was 20 times of the period of Zhai et al. On the other hand, total loading cycles of Zhai et al., 5 × 10⁶, was 50 times of the present study, 1 × 10⁵. The resolved shear stresses of both studies were almost same level. And because the specimen of Zhai et al. was a single crystal, the traversed length along the directions of the primary PSMs of Zhai et al. were expected to be much longer than the polycrystals of the present study. Nevertheless, the extrusion height of the present study was much higher than that of Zhai et al. Taking all factors into the consideration, we may be able to conclude that the high mobile dislocation density accompanied by the dislocation channeling effect inside the PSBs of the present specimen produce the high extrusions through the concentration of the dislocation glides and the vacancy transportations.

4. Appearance Changes of PSMs during the Loading of 0.6, 1.2 and 2.4 × 10⁵ Cycles with the Maximum Stress of 8.0 MPa

In order to investigate the macroscopic appearance changes of the PSMs during the cyclic loading, we interrupted the loading at 0.6, 1.2 and 2.4 × 10⁵ cycles and observed the PSMs morphology.

Figure 9 shows an optical micrograph of the surface morphology of the polycrystalline specimen (different specimen of Fig. 4) after the loading of 0.6 × 10⁵ cycles with the maximum stress of 8.0 MPa. By picking the highlighted “Grain A” and “Grain B” as examples, SEM observations of the PSMs inside the grains were performed as below.

Fig. 9

Optical micrograph of the surface morphology of the polycrystalline specimen (different specimen of Fig. 4) after the loading of 0.6 × 10⁵ cycles with the maximum stress of 8.0 MPa. SEM images of the PSMs inside the highlighted “Grain A” and “Grain B” were shown in Figs. 10 and 11, respectively. “LD” means the cyclic loading direction.

Figure 10 shows SEM images of PSMs inside the highlighted “Grain A” of Fig. 9 after the loadings of 0.6, 1.2 and 2.4 × 10⁵ cycles in (a), (b) and (c), respectively. Enlarged SEM images of (a), (b) and (c) are shown in (d), (e) and (f), respectively. Well-grown coarse primary PSMs consisting of the typical ribbon-like extrusions and intrusions had been developed. Besides the primary PSMs, some faint secondary slips were observed, but, between 0.6 and 1.2 × 10⁵ cycles, major difference was not identified. On the other hand, until the loading of 2.4 × 10⁵ cycles, because of the activated secondary slips, the shape of the preexisting primary PSMs had been drastically deformed. And, as indicated by the arrow “N”, the fresh but faint primary PSMs had appeared between the preexisting primary PSMs.

Fig. 10

SEM images showing PSMs inside the highlighted “Grain A” after the loadings of 0.6, 1.2 and 2.4 × 10⁵ cycles in (a), (b) and (c), respectively. Enlarged SEM images of (a), (b) and (c) are shown in (d), (e) and (f), respectively. Coarse PSMs consisting of the typical ribbon-like extrusions and intrusions had been developed. Besides the primary PSMs, some faint secondary slips were observed. The arrow “N” indicates the fresh but faint primary PSMs appeared between the preexisting primary PSMs.

Figure 11 shows SEM images of PSMs inside the highlighted “Grain B” of Fig. 9 after the loadings of 0.6, 1.2 and 2.4 × 10⁵ cycles in (a), (b) and (c), respectively. Enlarged SEM images of (a), (b) and (c) are shown in (d), (e) and (f), respectively. As seen in Fig. 10, well-grown coarse primary PSMs consisting of the typical ribbon-like extrusions and intrusions had been developed. Besides the primary PSMs, some faint secondary slips were also observed, but, between 0.6 and 1.2 × 10⁵ cycles, major difference was not identified. On the other hand, until the loading of 2.4 × 10⁵ cycles, because of the activated secondary slips, the primary PSMs had been deformed to be wavy shaped. As indicated by the arrow “N”, the fresh but faint primary PSMs had appeared between the preexisting primary PSMs. The similar surface morphologies were observed in the almost all grains.

Fig. 11

SEM images showing PSMs inside the highlighted “Grain B” after the loadings of 0.6, 1.2 and 2.4 × 10⁵ cycles in (a), (b) and (c), respectively. Enlarged SEM images of (a), (b) and (c) are shown in (d), (e) and (f), respectively. Coarse PSMs consisting of the typical ribbon-like extrusions and intrusions had been developed. Besides the primary PSMs, some faint secondary slips were observed. The arrow “N” indicates the fresh but faint primary PSMs appeared between the preexisting primary PSMs.

These results suggest that, during the cyclic loading, work-hardening structures which were observed in the uniaxially-tensile-deformed single crystals^36–40,45) had been created inside the PSBs until the loadings of around 10⁵ cycles and weakened or terminated the activities of the primary PSBs. On the other hand, under the further loadings, because of the accumulations of the strains due to the PSBs, the secondary slips were considered to be activated for the relaxation of the crystal rotations caused by the intergranular restrictions between the neighboring grains. Dislocation density of each secondary slip should be low, but a huge number of the secondary slips deformed the shapes of the preexisting primary PSMs. Therefore, inside the preexisting PSBs, we consider that the primary and the secondary dislocations react each other and create tangled structures. To understand the precise dislocation structures inside the work-hardened PSBs, as Tsuchida et al.⁴⁰⁾ conducted on the uniaxially-tensile-deformed aluminum single crystals, systematic 3D-TEM observations of the tangled structures must be performed in future.

Although any obvious long cracks were not identified inside the grains until the loading of 2.4 × 10⁵ cycles, as expressed in the next section, we recognized the well-grown cracks at GBs.

5. Several Interactions between PSB and GB under the Cyclic Loading

As mentioned in the Section 1, Liu et al.²⁹⁾ classified the PSB-GB interaction into the three categories, i.e., the dislocation transmission, the dislocation source activation, and the crack nucleation. In the present investigation, we confirmed the occurrences of the three events on the present polycrystalline specimens.

Figure 12 shows an optical micrograph of the surface morphology of the polycrystalline specimen (different specimen of Figs. 4 and 9) after the loading of 1.0 × 10⁵ cycles with the maximum stress of 6.2 MPa. Despite the low stress level, PSMs were observed in some grains. Detailed morphologies of the enclosed areas “A” and “B” are shown in Figs. 13 and 14, respectively.

Fig. 12

Optical micrograph of the surface morphology of the specimen (different specimen of Figs. 4 and 9) after the loading of 1 × 10⁵ cycles with the maximum stress of 6.2 MPa. Detailed morphologies of the enclosed area “A” and “B” are shown in Figs. 13 and 14, respectively. “LD” means the cyclic loading direction.

Fig. 13

(a) Optical micrograph of the enclosed area “A” of Fig. 12. (b) SEM image of the enclosed area of (a). PSMs of the “Grain A1” had been transmitting to the “Grain A2”. In the “Grain A2”, other PSBs had been activated at the intersections between the transmitting PSBs and the GB. (c) Enlarged SEM image of (b). (d) Further enlarged SEM image of (c).

Fig. 14

(a) Optical micrograph of the enclosed area “B” of Fig. 12. (b) SEM image of the enclosed area of (a). PSMs of the “Grain B1” had not been transmitting to the “Grain B2”. (c) Enlarged SEM image of (b). (d) Further enlarged SEM image of (c). Note that extrusion and tiny crack had been formed along the GB where the PSBs inside the “Grain B1” collided.

Figure 13(a) shows an optical micrograph of the enclosed area “A” of Fig. 12. “Grain A1” and “Grain A2” were sandwiching a GB. Figure 13(b) shows a SEM image of the enclosed area of Fig. 13(a). Figure 13(c) shows a SEM image of the enclosed area of Fig. 13(b), and Fig. 13(d) shows a SEM image of the enclosed area of Fig. 13(c). PSMs of the “Grain A1” had been transmitting to the “Grain A2”, and after the several micrometers’ invasion, tips of the PSMs had been tapered and their invasions had been terminated. On the other hand, the faint PSMs in the “Grain A2” had been activated at the intersections between the GB and the PSMs of the “Grain A1”.

Figure 14(a) shows an optical micrograph of the enclosed area “B” of Fig. 12. “Grain B1” and “Grain B2” were sandwiching a GB. Figure 14(b) shows a SEM image of the enclosed area of Fig. 14(a). Figure 14(c) shows a SEM image of the enclosed area of Fig. 14(b), and Fig. 14(d) shows a SEM image of the enclosed area of Fig. 14(c). PSMs of the “Grain B1” had “not” been transmitting to the “Grain B2”, but their tips had been terminated at the GB. And Fig. 14(d) clearly shows the formation of an extrusion and a tiny crack at the intersection of the GB and the PSM of the “Grain B1”. The lengths of the cracks were equivalent with the width of the PSMs. As Chlupová et al.²⁸⁾ expressed, PSBs produce not only the specific relief on the surface in the form of extrusions and intrusions but also a similar relief at GBs. These are considered to be the result of volume expansions due to the generations and migrations of a large number of vacancies. The vacancy model proposed by Liu et al.²⁹⁾ may be able to explain the formation mechanism of the cracks, but those cracks had not developed to the final failures at this stage.

Figure 15 shows the same optical micrograph of Fig. 9, i.e., surface morphology of the polycrystalline specimen after the loading of 0.6 × 10⁵ cycles with the maximum stress of 8.0 MPa. Although any obvious long cracks were not identified inside the grains at this stage, after the loading of 2.4 × 10⁵ cycles, we recognized the development of well-grown crack along the GB between the highlighted “Grain C” and “Grain D”. Figure 16(a) shows SEM image of the deep brittle-like crack observed after the loading of 2.4 × 10⁵ cycles at the GB between “Grain C” and “Grain D”. Figure 16(b) shows an enlarged image of the crack. This crack had already grown to the lengths of 0.8 mm. A huge number of faint PSMs were intersecting with the GB where the crack opened.

Fig. 15

Same optical micrograph of Fig. 9, i.e., the surface morphology of the polycrystalline specimen after the loading of 0.6 × 10⁵ cycles with the maximum stress of 8.0 MPa. After the loading of 2.4 × 10⁵ cycles, as shown in the next Fig. 16, the well-grown crack was observed at the GB between the highlighted “Grain C” and “Grain D”.

Fig. 16

(a) SEM image showing the deep brittle-like crack observed after the loading of 2.4 × 10⁵ cycles with the maximum stress of 8.0 MPa at the GB between “Grain C” and “Grain D”. (b) Enlarged image of the crack. A huge number of faint PSMs were intersecting with the GB where the crack opened.

Based on the Griffith fracture criterion, Mura⁴⁶⁾ described a simple critical stress σ_CR for the pancake-shaped crack opening as below.

  

\begin{equation} \sigma_{\textit{CR}} = \left\{\frac{\pi\mu\gamma}{(1 - \nu)a}\right\}^{1/2} \end{equation} (2)

Here, γ: surface energy per unit area, a: crack radius, μ: shear modulus, ν: Poisson’s ratio. We did not observe the initial lengths of the cracks. Based on the cracks along the GBs observed in Fig. 14, assuming the initial length of the crack as 7 µm (order of the PSM maximum width obtained in Section 3) and taking other parameters from the literature of Liu et al.,²⁹⁾ i.e., γ = 1.14 J/m², μ = 26.1 GPa, ν = 0.33, we can estimate σ_CR ≅ 200 MPa which is much higher than the applied maximum stress. However, as Liu et al.²⁹⁾ mentioned, the poor plastic compatibility introduced by the transportations of the residual dislocations and the vacancies leads to decrease of the grain boundary decohesion energy. Therefore, we can assume that the accumulation of the dislocations and the vacancies into the GBs leads to the energy reduction of the GBs as the interfaces, and, due to the cumulative strains until the loading of the present study, i.e., 2.4 × 10⁵ cycles, each tiny cracks formed at the intersections between GBs and PSMs link together and develop to the brittle-like cracks shown in Fig. 16.

6. Conclusion

Surface relief formation processes were examined on the high cycle-loaded coarse-grained aluminum polycrystals with point defect clusters by using optical microscope, AFM and SEM. In the present study, the push-and-pull cyclic loadings with the stress ratio of −1 were performed in air and at room temperature. Taking the present and previous results into our considerations, we developed the following conclusions.

1. (1)    Until the loading of 1 × 10⁵ cycles with the maximum stress of 8.0 MPa, the coarse ribbon-like primary PSMs consisting of extrusions and intrusions had been formed, and average extrusion height of the PSMs reached 2.0 µm. This value was much higher than that of the ordinary aluminum single crystal, i.e., 0.8 µm, after the loading of 5 × 10⁶ cycles.¹⁴⁾ The high mobile dislocation density accompanied by the dislocation channeling effect inside the PSBs were considered to produce the high extrusions.
2. (2)    Until the loadings to 2.4 × 10⁵ cycles with the maximum stress of 8.0 MPa, activities of the primary PSBs had been weakened or terminated, and instead, the secondary slips had been activated. Although the dislocation density of each secondary slips should be low, a huge number of the secondary slips deformed the shapes of the preexisting primary PSMs.
3. (3)    The occurrences of the three events of the PSB-GB interaction,²⁹⁾ i.e., the dislocation transmission, the dislocation source activation, and the tiny crack nucleation were confirmed after the loadings of 1.0 × 10⁵ cycles with the maximum stress of 6.2 MPa. And after the 2.4 × 10⁵ cycles with the maximum stress of 8.0 MPa, the deep brittle-like cracks along the GBs were observed. The accumulation of the dislocations and the vacancies into the GBs was considered to be the trigger for the energy reduction of the GBs as the interfaces and the brittle-like cracks formation.

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